Mercurial > hg > cfcfd3
changeset 1596:29f541ac46a6
Eilmer3 user guide: added description for the concave ramp (2D/cubic-ramp).
| author | Peter Jacobs <peterj@mech.uq.edu.au> |
|---|---|
| date | Mon, 26 May 2014 12:30:16 +1000 |
| parents | b846abad8a48 |
| children | 16f52c93bfad |
| files | examples/eilmer3/2D/cubic-ramp/cubic-ramp-edited.pdf examples/eilmer3/2D/cubic-ramp/cubic-ramp-edited.svg examples/eilmer3/user-guide/bibtex/compress.bib examples/eilmer3/user-guide/bibtex/gas_dynamic.bib examples/eilmer3/user-guide/cubic-ramp.tex examples/eilmer3/user-guide/eilmer3-user-guide.tex |
| diffstat | 6 files changed, 3212 insertions(+), 0 deletions(-) [+] |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/examples/eilmer3/user-guide/bibtex/compress.bib Mon May 26 12:30:16 2014 +1000 @@ -0,0 +1,2067 @@ +@string {arfm = "Annual Review of Fluid Mechanics"} +@string {jfm = "Journal of Fluid Mechanics"} +@string {jcp = "Journal of Computational Physics"} + +@string {pf = "The Physics of Fluids"} +@string {pfa = "The Physics of Fluids (A)"} +@string {pfb = "The Physics of Fluids (B)"} + +@string {caf = "Computers and Fluids"} +@string {cmame = " Computer Methods in Applied Mechanics and Engineering"} + +@string {taj = "The Aeronautical Journal"} + +@string {aiaaj = "A.I.A.A. Journal"} +@string {aiaajsr = "A.I.A.A. Journal of Spacecraft and Rockets"} +@string {aiaajpp = "A.I.A.A. Journal of Propulsion and Power"} +@string {aiaaja = "A.I.A.A. Journal of Aircraft"} +@string {aiaajtpht = "A.I.A.A. Journal of Thermophysics and Heat Transfer"} + +@string {ijnmf = "International Journal for Numerical Methods in Fluids"} +@string {ijnme = "International Journal for Numerical Methods in Engineering"} +@string {ijhff = "International Journal for Heat and Fluid Flow"} + +@string {siamssc = "SIAM Journal on Scientific and Statistical Computing"} +@string {siamna = "SIAM Journal on Numerical Analysis"} + +@string {nasatp = "NASA Technical Paper"} +@string {nasatm = "NASA Technical Memorandum"} +@string {nasacr = "NASA Contractor Report"} + +-aa- + +@TECHREPORT {abgrall_91a, + AUTHOR = {Abgrall, R.}, + TITLE = {Design of an essentially non-oscillatory reconstruction + procedure on finite-element type meshes.}, + INSTITUTION = {}, + YEAR = {1991}, + TYPE = {ICASE Report}, + NUMBER = {91-84}, + ADDRESS = {}, + ANNOTE = {} + } + +@INPROCEEDINGS {abgrall_merlo_91, + AUTHOR = {Abgrall, R. and Merlo, A.}, + TITLE = {Numerical simulations around models in hypersonic + wind tunnels.}, + BOOKTITLE = {Aerothermodynamics for Space Vehicles. SP-318.}, + YEAR = {1991}, + PAGES = {189--195}, + PUBLISHER = {European Space Agency}, + ANNOTE = {* multi-block solver} + } + +@TECHREPORT {anderson_etal_85, + AUTHOR = {Anderson, W. K. and Thomas, J. L. and van Leer, B.}, + TITLE = {A comparison of finite volume flux vector splittings + for the {Euler} equations.}, + INSTITUTION = {}, + YEAR = {1985}, + MONTH = { January }, + TYPE = {AIAA Paper}, + NUMBER = {85-0122}, + ADDRESS = {}, + ANNOTE = {* third-order upwind biased interpolation/reconstruction} + } + +@ARTICLE {anderson_bonhaus_93, + AUTHOR = { Anderson, W. K. and Bonhaus, D. L. }, + TITLE = { An implicit upwind algorithm for computing turbulent + flows on unstructured grids. }, + JOURNAL = caf, + YEAR = { 1993 }, + VOLUME = { 23 }, + NUMBER = { 1 }, + PAGES = { 1--21 }, + ANNOTE = {} + } + +@TECHREPORT {atkins_87, + AUTHOR = {Atkins, H. L.}, + TITLE = {Comparisons and applications of time-accurate + finite-volume methods for solving unsteady {Euler} equations.}, + INSTITUTION = {}, + YEAR = {1987}, + TYPE = {AIAA Paper}, + NUMBER = {87-0189}, + ADDRESS = {}, + ANNOTE = {* axisymmetric (but 2d) test case including radial + shock} + } + +@TECHREPORT {atkins_88, + AUTHOR = {Atkins, H. L.}, + TITLE = {Numerical and analytical study of the inlet + startup process in a shock tunnel environment. }, + INSTITUTION = {}, + YEAR = {1988}, + TYPE = {AIAA Paper}, + NUMBER = {88-0601}, + ADDRESS = {}, + ANNOTE = {} + } + +@TECHREPORT {atkins_89, + AUTHOR = {Atkins, H. L.}, + TITLE = {Analysis of a second-order-accurate finite-volume method + for temporally-growing compressible shear layers.}, + INSTITUTION = {}, + YEAR = {1989}, + TYPE = {AIAA Paper}, + NUMBER = {89-1809}, + ADDRESS = {}, + ANNOTE = {} + } + +-bb- + +@TECHREPORT {bardina_etal_85, + AUTHOR = {Bardina, J. and Venkatapathy, E. and Lombard, C. K.}, + TITLE = {Two dimensional and axisymmetric heat-transfer results + with the {CSCM} upwind implicit method.}, + INSTITUTION = {}, + YEAR = {1985}, + TYPE = {AIAA Paper}, + NUMBER = {85-0923}, + ADDRESS = {}, + ANNOTE = {} + } + +@ARTICLE {batina_93, + AUTHOR = {Batina, J. T.}, + TITLE = {Implicit upwind solution algorithms for the + three-dimensional unstructured meshes. }, + JOURNAL = aiaaj, + YEAR = {1993}, + VOLUME = {31}, + NUMBER = {5}, + PAGES = {801--805}, + ANNOTE = {} + } + +@ARTICLE { baum_lohner_94, + AUTHOR = { Baum, J. D. and Lohner, R. }, + TITLE = { Numerical simulation of shock-box interaction using adaptive + finite-element scheme. }, + JOURNAL = aiaaj, + YEAR = { 1994 }, + VOLUME = { 32 }, + NUMBER = { 4 }, + PAGES = { 682 }, + ANNOTE = { * very detailed calculations of what seem to be 2D flows } + } + +@ARTICLE {baysal_hoffman_92, + AUTHOR = {Baysal, O. and Hoffman, W. B.}, + TITLE = {Simulation of three-dimensional shear flow around a nozzle + at high speeds.}, + JOURNAL = {Transactions of the ASME, Journal of Fluids Engineering.}, + YEAR = {1992}, + VOLUME = {114}, + NUMBER = {}, + PAGES = {178--185}, + ANNOTE = {} + } + +@ARTICLE {benson_91, + AUTHOR = {Benson, D. J.}, + TITLE = {A new two-dimensional flux-limited shock viscosity + for impact calculations.}, + JOURNAL = {Computer Methods in Applied Mechanics and Engineering}, + YEAR = {1991}, + VOLUME = {93}, + NUMBER = {}, + PAGES = {39--95}, + ANNOTE = {} + } + +@ARTICLE {berman_etal_83, + AUTHOR = {Berman, H. A. and Anderson, J. D. and Drummond, J. P.}, + TITLE = {Supersonic flow over a rearward facing step with + transverse nonreacting hydrogen injection.}, + JOURNAL = aiaaj, + YEAR = {1983}, + VOLUME = {21}, + NUMBER = {12}, + PAGES = {1707--1713}, + ANNOTE = {} + } + +@TECHREPORT {boretti_90, + AUTHOR = {Boretti, A. A.}, + TITLE = {Two-dimensional {Euler} and {Navier}-{Stokes} + time accurate simulations of fan rotor flows.}, + INSTITUTION = {}, + YEAR = {1990}, + TYPE = nasatm, + NUMBER = {102402}, + ADDRESS = {}, + ANNOTE = {} + } + +-cc- + +@TECHREPORT {carpenter_89, + AUTHOR = {Carpenter, M. H.}, + TITLE = {Three-dimensional computations of cross-flow injection + and combustion in a supersonic flow.}, + INSTITUTION = {}, + YEAR = {1989}, + TYPE = {AIAA Paper}, + NUMBER = {89-1870}, + ADDRESS = {}, + ANNOTE = {* 3D version of SPARK} + } + +@ARTICLE {carpenter_90a, + AUTHOR = {Carpenter, M. H.}, + TITLE = {A high order compact numerical algorithm for supersonic + flows.}, + JOURNAL = {}, + YEAR = {1990}, + VOLUME = {}, + NUMBER = {}, + PAGES = {}, + ANNOTE = {* obtained directly from Mark} + } + +@ARTICLE {chakrabartty_89, + AUTHOR = {Chakrabartty, S. K.}, + TITLE = {Numerical solutions of {Navier}-{Stokes} equations for + two dimensional viscous compressible flows.}, + JOURNAL = aiaaj, + YEAR = {1989}, + VOLUME = {27}, + NUMBER = {7}, + PAGES = {843--844}, + ANNOTE = {* cell-vertex N-S scheme} + } + +@ARTICLE {chakrabartty_90, + AUTHOR = {Chakrabartty, S. K.}, + TITLE = {Vertex-based finite-volume solution of the + two-dimensional {Navier}-{Stokes} equations.}, + JOURNAL = aiaaj, + YEAR = {1990}, + VOLUME = {28}, + NUMBER = {10}, + PAGES = {1829--1831}, + ANNOTE = {} + } + +@ARTICLE {chang_etal_88, + AUTHOR = {Chang, C. -L. and Kronzon, Y. and Merkle, C. L.}, + TITLE = {Time-iterative solutions of viscous supersonic nozzle + flows.}, + JOURNAL = aiaaj, + YEAR = {1988}, + VOLUME = {26}, + NUMBER = {10}, + PAGES = {1208--1215}, + ANNOTE = {* steady state calculations + * upstream influence of back-pressure in the boundary layer + } + } + +@ARTICLE { chen_93, + AUTHOR = { Chen, H. }, + TITLE = { Discrete {Boltzmann} systems and fluid flows. }, + JOURNAL = { Computers in Physics }, + YEAR = { 1993 }, + VOLUME = { 7 }, + NUMBER = { 6 }, + PAGES = { 632--637 }, + ANNOTE = {} + } + +@TECHREPORT {chima_etal_86, + AUTHOR = {Chima, R. V. and Turkel, E. and Schaffer, S.}, + TITLE = {Comparisons of three explicit multigrid methods for the + {Euler} and {Navier}-{Stokes} equations.}, + INSTITUTION = {}, + YEAR = {1986}, + TYPE = nasatm, + NUMBER = {88878}, + ADDRESS = {}, + ANNOTE = {* also ICOMP-86-3 and AIAA-87-???? + * test case was a shock-boundary layer interaction + * hakkinen's data + } + } + +@TECHREPORT {colella_etal_89, + AUTHOR = {Colella, P. and Henderson, L. F. and Puckett, E. G.}, + TITLE = {A numerical study of shock wave refraction at a gas + interface.}, + INSTITUTION = {}, + YEAR = {1989}, + TYPE = {AIAA Paper}, + NUMBER = {89-1973-CP}, + ADDRESS = {}, + ANNOTE = {} + } + +@ARTICLE {colella_henderson_90, + AUTHOR = {Colella, P. and Henderson, L. F.}, + TITLE = {The {von} {Neumann} paradox for the diffraction + of weak shock waves.}, + JOURNAL = jfm, + YEAR = {1990}, + VOLUME = {213}, + NUMBER = {}, + PAGES = {71--94}, + ANNOTE = {} + } + +-dd- + +@TECHREPORT {dadone_grossman_91, + AUTHOR = {Dadone, A. and Grossman, B.}, + TITLE = {A rotated upwind scheme for the {Euler} equations.}, + INSTITUTION = {}, + YEAR = {1991}, + TYPE = {AIAA Paper}, + NUMBER = {91-0635}, + ADDRESS = {}, + ANNOTE = {} + } + +@ARTICLE {daripa_90, + AUTHOR = {Daripa, P.}, + TITLE = {On applications of a complex variable method in + compressible flows.}, + JOURNAL = jcp, + YEAR = {1990}, + VOLUME = {88}, + NUMBER = {}, + PAGES = {337--361}, + ANNOTE = {* does this hold possibilities for Contour Dynamics + type simulations??? + } + } + +@INPROCEEDINGS {davies_etal_89, + AUTHOR = {Davies, C. B. and Venkatapathy, E. and Deiwert, G. S.}, + TITLE = {{SAGE}. A {2-D} self-adaptive grid evolution code and its + application in computational fluid dynamics.}, + BOOKTITLE = {{NASA} Computational Fluid Dynamics Conference}, + YEAR = {1989}, + PAGES = {239--253}, + PUBLISHER = {}, + ANNOTE = {* this is only a collection of slides -- + very little detail} + } + +@TECHREPORT {decker_turkel_90, + AUTHOR = {Decker, N. H. and Turkel, E.}, + TITLE = {Multigrid for hypersonic inviscid flows.}, + INSTITUTION = {}, + YEAR = {1990}, + TYPE = {ICASE Report}, + NUMBER = {90-54}, + ADDRESS = {}, + ANNOTE = {} + } + +@ARTICLE {dezeeuw_powell_93, + AUTHOR = {De Zeeuw, D. and Powell, K. G.}, + TITLE = {An adaptively refined cartesian mesh solver for the + {Euler} equations.}, + JOURNAL = jcp, + YEAR = {1993}, + VOLUME = {104}, + NUMBER = {1}, + PAGES = {56--68}, + ANNOTE = {} + } + +@ARTICLE { drikakis_tsangaris_93, + AUTHOR = { Drikakis, D. and Tsangaris, S. }, + TITLE = { Real gas effects for compressible nozzle flows. }, + JOURNAL = { Transactions of the ASME. Journal of Fluids Engineering. }, + YEAR = { 1993 }, + VOLUME = { 115 }, + NUMBER = {}, + PAGES = { 115--120 }, + ANNOTE = {} + } + +@ARTICLE {durlofsky_etal_92, + AUTHOR = {Durlofsky, L. J. and Engquist, B. and Osher, S.}, + TITLE = {Triangle based adaptive stencils for the solution of + hyperbolic conservation laws.}, + JOURNAL = jcp, + YEAR = {1992}, + VOLUME = {98}, + NUMBER = {}, + PAGES = {64--73}, + ANNOTE = {* simple scheme to get second order on unstructured + triangular meshes + } + } + +-ee- + +@TECHREPORT {eberle_93, + AUTHOR = { Eberle, A. }, + TITLE = { Recent {CFD} enhancements for structured mesh + {Navier}-{Stokes} and {Euler} solvers. }, + INSTITUTION = {}, + YEAR = { 1993 }, + TYPE = { AIAA Paper }, + NUMBER = { 93-5068 }, + ADDRESS = {}, + ANNOTE = { * smooth limiters make a difference } + } + +@ARTICLE { eidelman_etal_1984a, + AUTHOR = { Eidelman, S. and Colella, P. and Shreeve, R. P. }, + TITLE = { Application of the {Godunov} method and its second-order + extension to cascade flow modelling. }, + JOURNAL = aiaaj, + YEAR = { 1984 }, + VOLUME = { 22 }, + NUMBER = { 11 }, + PAGES = { 1609--1615 }, + ANNOTE = {} + } + +@INPROCEEDINGS {esser_gronig_87, + AUTHOR = {Esser, B. and Gronig, H.}, + TITLE = {Equilibrium shock tube flow of real gases.}, + BOOKTITLE = {Shock Tubes and Waves.}, + YEAR = {1987}, + PAGES = {663--669}, + PUBLISHER = {}, + ANNOTE = {* real gas riemann solver + * iterative - secant method + * exact wave relations used for both shocks and expansions} + } + +-ff- + +@INPROCEEDINGS {falcovitz_birman_93, + AUTHOR = {Falcovitz, J. and Birman, A.}, + TITLE = {A singularities tracking conservation law scheme for + compressible duct flows.}, + BOOKTITLE = {Proceedings of the Eighteenth International Symposium + on Shock Waves, Sendai.}, + YEAR = {1991}, + PAGES = {1107--1111}, + PUBLISHER = {}, + ANNOTE = {} + } + +@ARTICLE {fenno_etal_92, + AUTHOR = {Fenno, C. C. and Street, C. L. and Hassan, H. A.}, + TITLE = {Use of finite volume schemes for transition simulation.}, + JOURNAL = aiaaj, + YEAR = {1992}, + VOLUME = {30}, + NUMBER = {4}, + PAGES = {1122--1125}, + ANNOTE = {} + } + +@INPROCEEDINGS {flores_89, + AUTHOR = {Flores, J.}, + TITLE = {The simulation of hypersonic flow using a zonal + approach.}, + BOOKTITLE = {Tenth Australasian Fluid Mechanics Conference, + Melbourne.}, + YEAR = {1989}, + PAGES = {6.33--6.36}, + PUBLISHER = {}, + ANNOTE = {} + } + +@ARTICLE {fouladi_baysal_92, + AUTHOR = {Fouladi, K. and Baysal, O.}, + TITLE = {Viscous simulation method for unsteady flows past + multicomponent configurations.}, + JOURNAL = {Transactions of the ASME, Journal of Fluids Engineering.}, + YEAR = {1992}, + VOLUME = {114}, + NUMBER = {}, + PAGES = {161--169}, + ANNOTE = {} + } + +-gg- + +@TECHREPORT {giles_83, + AUTHOR = {Giles, M.}, + TITLE = {{Eigenmode} analysis of unsteady one-dimensional {Euler} + equations.}, + INSTITUTION = {}, + YEAR = {1983}, + TYPE = {NASA Contractor Report}, + NUMBER = {172217}, + ADDRESS = {}, + ANNOTE = {} + } + +@TECHREPORT {giles_88, + AUTHOR = {Giles, M.}, + TITLE = {Non-reflecting boundary conditions for the {Euler} + equations.}, + INSTITUTION = {}, + YEAR = {1988}, + TYPE = {CFDL Report}, + NUMBER = {88-1}, + ADDRESS = {Department of Aeronautics and Astronautics, MIT}, + ANNOTE = {} + } + +@TECHREPORT {giles_89, + AUTHOR = {Giles, M.}, + TITLE = {Non-reflecting boundary conditions for {Euler} equation + calculations.}, + INSTITUTION = {}, + YEAR = {1989}, + TYPE = {AIAA Paper}, + NUMBER = {89-1942-CP}, + ADDRESS = {}, + ANNOTE = {} + } + +@ARTICLE {giles_90, + AUTHOR = {Giles, M. B.}, + TITLE = {Nonreflecting boundary conditions for {Euler} equation + calculations.}, + JOURNAL = aiaaj, + YEAR = {1990}, + VOLUME = {28}, + NUMBER = {12}, + PAGES = {2050--2058}, + ANNOTE = {* seems to be the revised version of AIAA-89-1942} + } + +@ARTICLE {glaister_88, + AUTHOR = {Glaister, P.}, + TITLE = {Flux difference splitting for the {Euler} equations + with axial symmetry.}, + JOURNAL = {Journal of Engineering Mathematics}, + YEAR = {1988}, + VOLUME = {22}, + NUMBER = {2}, + PAGES = {107--121}, + ANNOTE = {* spherical shock test case } + } + +@ARTICLE {gnoffo_83, + AUTHOR = {Gnoffo, P. A.}, + TITLE = {A finite-volume, adaptive grid algorithm applied + to planetary entry flowfields.}, + JOURNAL = aiaaj, + YEAR = {1983}, + VOLUME = {21}, + NUMBER = {9}, + PAGES = {1249--1254}, + ANNOTE = {} + } + +@TECHREPORT {gnoffo_90a, + AUTHOR = {Gnoffo, P. A.}, + TITLE = {An upwind-biased point implicit relaxation algorithm + for viscous, compressible perfect-gas flows.}, + INSTITUTION = {}, + YEAR = {1990}, + TYPE = nasatp, + NUMBER = {2953}, + ADDRESS = {}, + ANNOTE = {* CFD for the aerobrake experiment} + } + +@INPROCEEDINGS {grasso_etal_90, + AUTHOR = {Grasso, F. and Bassi, F. and Harten, A.}, + TITLE = {ENO schemes for viscous high speed flows.}, + BOOKTITLE = {12th International Conference on Numerical Methods + in Fluid Dynamics}, + YEAR = {1990}, + PAGES = {}, + PUBLISHER = {}, + ANNOTE = {} + } + +@INPROCEEDINGS {grasso_magi_91, + AUTHOR = {Grasso, F. and Magi, V.}, + TITLE = {Numerical methodologies for the compressible + {Navier}-{Stokes} equations for two-phase flows.}, + BOOKTITLE = {Modern Research Topics in Aerospace Propulsion}, + YEAR = {1991}, + PAGES = {227--250}, + PUBLISHER = {Springer-Verlag}, + ANNOTE = {} + } + +@ARTICLE {grasso_etal_92, + AUTHOR = {Grasso, F. and Marini, M. and Passalacqua, M.}, + TITLE = {Viscous high-speed flow computations by adaptive mesh + embedding techniques.}, + JOURNAL = aiaaj, + YEAR = {1992}, + VOLUME = {30}, + NUMBER = {7}, + PAGES = {1780--1788}, + ANNOTE = {} + } + +@ARTICLE {grasso_marini_93, + AUTHOR = {Grasso, F. and Marini, M.}, + TITLE = {Multiblock implicit total variation diminishing solution + of high-speed internal flows.}, + JOURNAL = aiaajpp, + YEAR = {1993}, + VOLUME = {9}, + NUMBER = {2}, + PAGES = {255--262}, + ANNOTE = {} + } + +-hh- + +@ARTICLE {hasen_82, + AUTHOR = {Hasen, G. A.}, + TITLE = {{Navier}-{Stokes} solutions for an axisymmetric nozzle.}, + JOURNAL = aiaaj, + YEAR = {1982}, + VOLUME = {20}, + NUMBER = {9}, + PAGES = {1219--1227}, + ANNOTE = {* was also paper AIAA 81-1474R + * MacCormack scheme for axisymmetric flow. + } + } + +@TECHREPORT {hawkin_gottlieb_90, + AUTHOR = {Hawken, D. F. and Gottlieb, J. J.}, + TITLE = {Prediction of two-dimensional time-dependent gasdynamic + flows for hypersonic studies.}, + INSTITUTION = {}, + YEAR = {1990}, + TYPE = {UTIAS Report}, + NUMBER = {335}, + ADDRESS = {}, + ANNOTE = {* inlet simulations with Euler calculations + * time-dependent + } + } + +@ARTICLE {hedstrom_79, + AUTHOR = {Hedstrom, G. W.}, + TITLE = {Nonreflecting boundary conditions for nonlinear + hyperbolic systems.}, + JOURNAL = jcp, + YEAR = {1979}, + VOLUME = {30}, + NUMBER = {}, + PAGES = {222--237}, + ANNOTE = {} + } + +@INPROCEEDINGS {hehmsoth_demmig_87, + AUTHOR = {Hehmsoth, H. -H. and Demmig, F.}, + TITLE = {Comparative study of numerical methods for two-phase + flow-shock front propagation.}, + BOOKTITLE = {Shock Tubes and Waves.}, + YEAR = {1987}, + PAGES = {655--661}, + PUBLISHER = {}, + ANNOTE = {} + } + +@TECHREPORT {hoffman_etal_87, + AUTHOR = {Hoffman, J. J. and Birch, S. F. and Hopcroft, R. G. + and Holcomb, J. E.}, + TITLE = {{Navier}-{Stokes} calculations of rocket base flows.}, + INSTITUTION = {}, + YEAR = {1987}, + TYPE = {AIAA Paper}, + NUMBER = {87-0466}, + ADDRESS = {}, + ANNOTE = {* Navier-Stokes solver to go with the zonal grid paper + of holcomb_87} + } + +@INPROCEEDINGS {hui_91, + AUTHOR = {Hui, W. H.}, + TITLE = {Accurate computation of steady discontinuous flow.}, + BOOKTITLE = {Proceedings of the Asian Pacific Conference on + Computational Mechanics, Hong Kong}, + YEAR = {1991}, + PAGES = {1499--1504}, + PUBLISHER = {A. A. Balkema}, + ANNOTE = {} + } + +@ARTICLE {hui_loh_92, + AUTHOR = {Hui, W. H. and Loh, C. Y.}, + TITLE = {A new {Lagrangian} method for steady supersonic flow + computation Part II. Slip-line resolution.}, + JOURNAL = jcp, + YEAR = {1992}, + VOLUME = {103}, + NUMBER = {2}, + PAGES = {450--464}, + ANNOTE = {} + } + +@TECHREPORT {hung_maccormack_75, + AUTHOR = {Hung, C. M. and MacCormack, R. W.}, + TITLE = {Numerical solutions of supersonic and hypersonic + laminar flows over a two-dimensional compression corner.}, + INSTITUTION = {}, + YEAR = {1975}, + TYPE = {AIAA Paper}, + NUMBER = {75-2}, + ADDRESS = {}, + ANNOTE = {* wedge induced separation + * comparison with Holden's data + } + } + +@ARTICLE {hussaini_etal_80, + AUTHOR = {Hussaini, M. Y. and Baldwin, B. S. and MacCormack, R. W.}, + TITLE = {Asymptotic features of shock-wave boundary-layer + interaction.}, + JOURNAL = aiaaj, + YEAR = {1980}, + VOLUME = {18}, + NUMBER = {8}, + PAGES = {1014--1016}, + ANNOTE = {* have used asymptotic solutions for the + free-interaction problem to check the accuracy of the + numerical simulations. + * however, the more accurate, lower Re numerical solutions + have pressure profiles which are further away from the + asymptotic solution than less accurate high Re numerical solns. + } + } + +@ARTICLE {hwang_liu_92, + AUTHOR = {Hwang, C. J. and Liu, J. L.}, + TITLE = {Locally implicit hybrid algorithm for steady and unsteady + viscous flows.}, + JOURNAL = aiaaj, + YEAR = {1992}, + VOLUME = {30}, + NUMBER = {5}, + PAGES = {1228--1236}, + ANNOTE = {} + } + +@ARTICLE {hwang_wu_92, + AUTHOR = {Hwang, C. J. and Wu, S. J.}, + TITLE = {Global and local remeshing algorithms for compressible + flows.}, + JOURNAL = jcp, + YEAR = {1992}, + VOLUME = {102}, + NUMBER = {1}, + PAGES = {98--113}, + ANNOTE = {} + } + +@ARTICLE {hwang_wu_93, + AUTHOR = {Hwang, C. J. and Wu, S. J.}, + TITLE = {Adaptive finite volume upwind approach on mixed + quadrilateral-triangular meshes.}, + JOURNAL = aiaaj, + YEAR = {1993}, + VOLUME = {31}, + NUMBER = {1}, + PAGES = {61--67}, + ANNOTE = {} + } + +-ii- +-jj- + +@TECHREPORT {jameson_etal_81, + AUTHOR = {Jameson, A. and Schmidt, W. and Turkel, E.}, + TITLE = {Numerical solutions of the {Euler} equations by finite + volume methods using {Runge}-{Kutta} time-stepping schemes.}, + INSTITUTION = {}, + YEAR = {1981}, + TYPE = {AIAA Paper}, + NUMBER = {81-1259}, + ADDRESS = {}, + ANNOTE = {* one of the classics} + } + +-kk- + +@ARTICLE {Kanarachos_vournas_93, + AUTHOR = { Kanarachos, A. E. and Vournas, I. P. }, + TITLE = { Multigrid technique for the compressible {Euler} and + {Navier}-{Stokes} equations. }, + JOURNAL = { Engineering Computations }, + YEAR = {1993}, + VOLUME = {10}, + NUMBER = {2}, + PAGES = {123--137}, + ANNOTE = {} + } + +@ARTICLE {katz_shaughnessy_90a, + AUTHOR = {Katz, I. M. and Shaughnessy, E. J.}, + TITLE = {Computer aided analysis of {1-D} compressible flow + problems in a {Lagrangian} particle description using + the Alpha method.}, + JOURNAL = caf, + YEAR = {1990}, + VOLUME = {18}, + NUMBER = {1}, + PAGES = {75--101}, + ANNOTE = {} + } + +@ARTICLE {katz_shaughnessy_90b, + AUTHOR = {Katz, I. M. and Shaughnessy, E. J.}, + TITLE = {The equations of {1-D} compressible flow with area change + in a {Lagrangian} particle description.}, + JOURNAL = caf, + YEAR = {1990}, + VOLUME = {18}, + NUMBER = {2}, + PAGES = {183--190}, + ANNOTE = {} + } + +@ARTICLE {kashimura_etal_86, + AUTHOR = {Kashimura, H. and Iwata, N. and Nishida, M.}, + TITLE = {Numerical analysis of the wave propagation in a duct with + an area change by the random choice method.}, + JOURNAL = {Bulletin of the JSME}, + YEAR = {1986}, + VOLUME = {29}, + NUMBER = {251}, + PAGES = {1440--1445}, + ANNOTE = {} + } + +@TECHREPORT {kumar_84, + AUTHOR = {Kumar, A.}, + TITLE = {User's guide for {NASCRIN}: A vectorized code for + calculating two-dimensional supersonic internal flow fields.}, + INSTITUTION = {}, + YEAR = {1984}, + TYPE = nasatm, + NUMBER = {85708}, + ADDRESS = {}, + ANNOTE = {} + } + +@TECHREPORT {kumar_etal_89, + AUTHOR = {Kumar, A. and Anderson, E. C. and Korte, J. J.}, + TITLE = {A need for a new {CFD} based hypersonic wind tunnel + nozzle design procedure.}, + INSTITUTION = {}, + YEAR = {1989}, + TYPE = {Informal Report}, + NUMBER = {}, + ADDRESS = {}, + ANNOTE = {* 72nd Semi-Annual meeting of the Supersonic Tunnel + Association, Princeton University, October 3&4 1989. + * not to be referenced} + } + +@TECHREPORT {kuruvila_anderson_85, + AUTHOR = {Kuruvila, G. and Anderson, J. D.}, + TITLE = {A study of the effects of numerical dissipation + on the calculation of supersonic separated flows.}, + INSTITUTION = {}, + YEAR = {1985}, + TYPE = {AIAA Paper}, + NUMBER = {85-0301}, + ADDRESS = {}, + ANNOTE = {} + } + +-ll- + +@ARTICLE {lappas_etal_93, + AUTHOR = {Lappas, T. Leonard, A. and Dimotakis, P. E.}, + TITLE = {An adaptive {Lagrangian} method for computing {1D} + reacting and non-reacting flows.}, + JOURNAL = jcp, + YEAR = {1993}, + VOLUME = {104}, + NUMBER = {2}, + PAGES = {361--376}, + ANNOTE = {} + } + +@TECHREPORT {lee_batina_91, + AUTHOR = {Lee, E. M. and Batina, J. T.}, + TITLE = {Conical {Euler} methodology for unsteady vortical + flows about rolling delta wings.}, + INSTITUTION = {}, + YEAR = {1991}, + TYPE = {AIAA Paper}, + NUMBER = {91-0730}, + ADDRESS = {}, + ANNOTE = {} + } + +@TECHREPORT {li_83, + AUTHOR = {Li, C. P.}, + TITLE = {On a finite-difference method for solving unsteady + viscous flow problems.}, + INSTITUTION = {}, + YEAR = {1983}, + TYPE = {AIAA Paper}, + NUMBER = {83-0560}, + ADDRESS = {}, + ANNOTE = {* has some interesting test cases including the + shock/separated-boundary-layer problem. + } + } + +@ARTICLE {loh_liou_93, + AUTHOR = {Loh, C. -Y. and Liou, M. -S.}, + TITLE = {Lagrangian solution of supersonic real gas flows.}, + JOURNAL = jcp, + YEAR = {1993}, + VOLUME = {104}, + NUMBER = {1}, + PAGES = {150--161}, + ANNOTE = {} + } + +@INPROCEEDINGS {lohner_86, + AUTHOR = {Lohner, R.}, + TITLE = {{FEM-FCT} and adaptive refinement schemes for strongly + unsteady flows.}, + BOOKTITLE = {Numerical Methods for Compressible Flows - + Finite Difference, Element and Volume Techniques}, + YEAR = {1986}, + PAGES = {93--114}, + PUBLISHER = {The American Society of Mechanical Engineers}, + ANNOTE = {* adaptive grid procedure + criteria for refinement} + } + +@TECHREPORT {lohner_etal_89, + AUTHOR = {Lohner, R. and Baum, J. D. and Loth, E. and + Ramamurti, R.}, + TITLE = {A finite element solver for axisymmetric compressible + flows.}, + INSTITUTION = {}, + YEAR = {1989}, + TYPE = {AIAA Paper}, + NUMBER = {89-1794}, + ADDRESS = {}, + ANNOTE = {* extension to axi-symmetric flow + * high order interpolation of all unknowns + * transient and steady flows. + * subsonic, transonic and supersonic + } + } + +@ARTICLE {long_91, + AUTHOR = {Long, L. N.}, + TITLE = {{Navier}-{Stokes} and {Monte} {Carlo} results for + hypersonic flow.}, + JOURNAL = aiaaj, + YEAR = {1991}, + VOLUME = {29}, + NUMBER = {2}, + PAGES = {200--207}, + ANNOTE = {* mentions rule for y+ + * mentions viscous time-step limitation + } + } + +-mm- + +@TECHREPORT {maccormack_69, + AUTHOR = {MacCormack, R. W.}, + TITLE = {The effect of viscosity in hypervelocity impact + cratering.}, + INSTITUTION = {}, + YEAR = {1969}, + TYPE = {AIAA Paper}, + NUMBER = {69-354}, + ADDRESS = {}, + ANNOTE = {* this seems to be the starting point for the technique + of the same name + * it is an adaption of the Lax-Wendroff 2nd order technique + } + } + +@INPROCEEDINGS {maccormack_71, + AUTHOR = {MacCormack, R. W.}, + TITLE = {Numerical solution of the interaction of a shock wave + with a laminar boundary layer.}, + BOOKTITLE = {Lecture Notes in Physics, Vol. 8}, + YEAR = {1971}, + PAGES = {151--163}, + PUBLISHER = {Springer-Verlag}, + ANNOTE = {} + } + +@TECHREPORT {maccormack_baldwin_75, + AUTHOR = {MacCormack, R. W. and Baldwin, B. S.}, + TITLE = {A numerical method for solving the {Navier}-{Stokes} + equations with application to shock-boundary layer + interactions.}, + INSTITUTION = {}, + YEAR = {1975}, + TYPE = {AIAA Paper}, + NUMBER = {75-1}, + ADDRESS = {}, + ANNOTE = {* test case Hakkinen's 59 data + * steady state limit only + } + } + +@TECHREPORT {maccormack_81, + AUTHOR = {MacCormack, R. W.}, + TITLE = {A numerical method for solving the equations of + compressible flow.}, + INSTITUTION = {}, + YEAR = {1981}, + TYPE = {AIAA Paper}, + NUMBER = {81-0110}, + ADDRESS = {}, + ANNOTE = {* implicit extension to the 1969 method + * example used -- laminar BL and oblique shock + * comparisons don't tell much + * computed pressures rise faster than measurements + } + } + +@ARTICLE {maccormack_82, + AUTHOR = {MacCormack, R. W.}, + TITLE = {A numerical method for solving the equations of + compressible flow.}, + JOURNAL = aiaaj, + YEAR = {1982}, + VOLUME = {20}, + NUMBER = {9}, + PAGES = {1275--1281}, + ANNOTE = {* presented as AIAA-81-0110} + } + +@ARTICLE {maccormack_lomax_??, + AUTHOR = {MacCormack, R. W. and Lomax, H.}, + TITLE = {Numerical solution of compressible viscous flows.}, + JOURNAL = {Annual Review of Fluid Mechanics}, + YEAR = {}, + VOLUME = {11}, + NUMBER = {}, + PAGES = {289--316}, + ANNOTE = {} + } + +@ARTICLE {marchant_weatherill_93, + AUTHOR = { Marchant, M. J. and Weatherill, N. P. }, + TITLE = { Adaptivity techniques for compressible inviscid flows. }, + JOURNAL = cmame, + YEAR = {1993}, + VOLUME = {106}, + NUMBER = {1-2}, + PAGES = {83--106}, + ANNOTE = {} + } + +@TECHREPORT {mavriplis_etal_89, + AUTHOR = {Mavriplis, D. J. and Jameson, A. and Martinelli, L.}, + TITLE = {Multigrid solution of the {Navier}-{Stokes} equations + on triangular meshes.}, + INSTITUTION = {}, + YEAR = {1989}, + TYPE = {ICASE Report}, + NUMBER = {89-11}, + ADDRESS = {}, + ANNOTE = {} + } + +@TECHREPORT {mavriplis_90a, + AUTHOR = {Mavriplis, D. J.}, + TITLE = {{Euler} and {Navier}-{Stokes} computations for + two-dimensional geometries using unstructured meshes.}, + INSTITUTION = {}, + YEAR = {1990}, + TYPE = {ICASE Report}, + NUMBER = {90-3}, + ADDRESS = {}, + ANNOTE = {} + } + +@TECHREPORT {mavriplis_91b, + AUTHOR = {Mavriplis, D. J.}, + TITLE = {Three-dimensional unstructured multigrid for the + {Euler} equations.}, + INSTITUTION = {}, + YEAR = {1991}, + TYPE = {ICASE Report}, + NUMBER = {91-41}, + ADDRESS = {}, + ANNOTE = {} + } + +@ARTICLE {mavriplis_92a, + AUTHOR = {Mavriplis, D. J.}, + TITLE = {Three-dimensional unstructured multigrid for the {Euler} + equations.}, + JOURNAL = aiaaj, + YEAR = {1992}, + VOLUME = {30}, + NUMBER = {7}, + PAGES = {1753--1761}, + ANNOTE = {} + } + +@ARTICLE {mcguirk_page_90, + AUTHOR = {McGuirk, J. J. and Page, G. J.}, + TITLE = {Shock capturing using a pressure-correction method.}, + JOURNAL = aiaaj, + YEAR = {1990}, + VOLUME = {28}, + NUMBER = {10}, + PAGES = {1751--1757}, + ANNOTE = {} + } + +@INPROCEEDINGS {milthorpe_91, + AUTHOR = {Milthorpe, J. F.}, + TITLE = {Numerical simulation of two-dimensional and axi-symmetric + compressible flows.}, + BOOKTITLE = {18th International Symposium on Shock Waves}, + YEAR = {1991}, + PAGES = {}, + PUBLISHER = {}, + ANNOTE = {* seems to ba a cartesian mesh code} + } + +@ARTICLE {milthorpe_92, + AUTHOR = {Milthorpe, J. F.}, + TITLE = {Simulation of supersonic and hypersonic flows.}, + JOURNAL = ijnmf, + YEAR = {1992}, + VOLUME = {14}, + NUMBER = {}, + PAGES = {267--288}, + ANNOTE = {} + } + +@ARTICLE {mitty_etal_93, + AUTHOR = {Mitty, T. J. and Jameson, A. and Baker, T. J.}, + TITLE = {Solution of three-dimensional supersonic flowfields + via adapting unstructured meshes. }, + JOURNAL = caf, + YEAR = {1993}, + VOLUME = {22}, + NUMBER = {2/3}, + PAGES = {271--283}, + ANNOTE = {} + } + +@INPROCEEDINGS {munz_87, + AUTHOR = {Munz, C. -D.}, + TITLE = {Two-step schemes for the {Euler} equations and numerical + experiments on the stability of converging cylindrical + shock waves.}, + BOOKTITLE = {Shock Tubes and Waves.}, + YEAR = {1987}, + PAGES = {685--691}, + PUBLISHER = {}, + ANNOTE = {} + } + +-nn- + +@TECHREPORT {netterfield_91, + AUTHOR = {Netterfield, M. P.}, + TITLE = {Computation of the aerodynamics of spinning bodies + using a point-implicit method.}, + INSTITUTION = {}, + YEAR = {1991}, + TYPE = {AIAA Paper}, + NUMBER = {91-0339}, + ADDRESS = {}, + ANNOTE = {* Fluid Gravity Engineering Ltd, Witley, Surry, UK} + } + +@INPROCEEDINGS {netterfield_91b, + AUTHOR = {Netterfield, M. P.}, + TITLE = {Hypersonic aerothermodynamic computations using a + point-implicit {TVD} method.}, + BOOKTITLE = {Aerothermodynamics for Space Vehicles. SP-318.}, + YEAR = {1991}, + PAGES = {259--266}, + PUBLISHER = {European Space Agency}, + ANNOTE = {} + } + +-oo- + +@ARTICLE {obayashi_92, + AUTHOR = {Obayashi, S.}, + TITLE = {Freestream capturing for moving coordinates in three + dimensions.}, + JOURNAL = aiaaj, + YEAR = {1992}, + VOLUME = {30}, + NUMBER = {4}, + PAGES = {1125--1128}, + ANNOTE = {} + } + +-pp- + +@ARTICLE {pan_cheng_93, + AUTHOR = { Pan, D. and Cheng, J. -C. }, + TITLE = { A second-order upwind finite-volume method for the + {Euler} solution on unstructured triangular meshes. }, + JOURNAL = ijnmf, + YEAR = {1993}, + VOLUME = {16}, + NUMBER = {}, + PAGES = {1079--1098}, + ANNOTE = {} + } + +@ARTICLE {peace_shaw_92, + AUTHOR = {Peace, A. J. and Shaw, J. A.}, + TITLE = {The modelling of aerodynamic flows by solution of the + {Euler} equations on mixed polyhedral grids.}, + JOURNAL = ijnme, + YEAR = {1992}, + VOLUME = {35}, + NUMBER = {10}, + PAGES = {2003--2029}, + ANNOTE = {} + } + +@TECHREPORT {peery_imlay_88, + AUTHOR = {Peery, K. M. and Imlay, S. T.}, + TITLE = {Blunt-body flow simulations.}, + INSTITUTION = {}, + YEAR = {1988}, + TYPE = {AIAA Paper}, + NUMBER = {88-2904}, + ADDRESS = {}, + ANNOTE = {* carbuncle problem with Roe's approx. Riemann solver} + } + +@TECHREPORT {peraire_etal_88, + AUTHOR = {Peraire, J. and Peiro, J. and Formaggia, L. and + Morgan, K. and Zienkiewicz, O. C.}, + TITLE = {Finite element {Euler} computations in three dimensions.}, + INSTITUTION = {}, + YEAR = {1988}, + TYPE = {AIAA Paper}, + NUMBER = {88--0032}, + ADDRESS = {}, + ANNOTE = {} + } + +@ARTICLE {peraire_etal_93, + AUTHOR = { Peraire, J. and Peiro, J. and Morgan, K. }, + TITLE = { Finite element multigrid solution of {Euler} flows + past installed aaero-engines. }, + JOURNAL = {Computational Mechanics}, + YEAR = {1993}, + VOLUME = {11}, + NUMBER = {5/6}, + PAGES = {433--451}, + ANNOTE = {} + } + +@INPROCEEDINGS {pollet_drouin_91, + AUTHOR = {Pollet, M. and Drouin, N.}, + TITLE = {Comparison of transport schemes for {Navier}-{Stokes} + equations application to rocket propulsion.}, + BOOKTITLE = {Numerical Methods is Laminar and Turbulent Flow. + Volume 7, Part 2.}, + YEAR = {1991}, + PAGES = {1496}, + PUBLISHER = {Pineridge Press}, + ANNOTE = {} + } + +@ARTICLE {pordal_etal_92, + AUTHOR = {Pordal, H. S. and Khosla, P. K. and Rubin, S. G.}, + TITLE = {A flux-split solution procedure for unsteady inlet + flow calculations.}, + JOURNAL = {Transactions of the ASME, Journal of Fluids Engineering.}, + YEAR = {1992}, + VOLUME = {114}, + NUMBER = {}, + PAGES = {198--204}, + ANNOTE = {} + } + +-qq- + +@TECHREPORT {quirk_92a, + AUTHOR = {Quirk, J. J.}, + TITLE = {An alternative to unstructured grids for computing gas + dynamic flows around arbitrarily complex two-dimensional + bodies.}, + INSTITUTION = {}, + YEAR = {1992}, + TYPE = {ICASE Report}, + NUMBER = {92-7}, + ADDRESS = {}, + ANNOTE = {* cartesian mesh with cut cells} + } + +@ARTICLE { quirk_93, + AUTHOR = { Quirk, J. J. }, + TITLE = { An alternative to unstructured grids for computing + gas dynamic flows around arbitrarily complex two-dimensional + bodies. }, + JOURNAL = caf, + YEAR = { 1993 }, + VOLUME = { 23 }, + NUMBER = { 1 }, + PAGES = { 125--142 }, + ANNOTE = {} + } + +-rr- + +@TECHREPORT {radespiel_swanson_91, + AUTHOR = {Radespiel, R. and Swanson, R. C.}, + TITLE = {Progress with multigrid schemes for hypersonic flow + problems.}, + INSTITUTION = {}, + YEAR = {1991}, + TYPE = {ICASE Report}, + NUMBER = {91-89}, + ADDRESS = {}, + ANNOTE = {} + } + +@ARTICLE {radespiel_etal_90, + AUTHOR = {Radespiel, R. and Rossow, C. and Swanson, R. C.}, + TITLE = {Efficient cell-vertex multigrid scheme for the + three-dimensional {Navier}-{Stokes} equations.}, + JOURNAL = aiaaj, + YEAR = {1990}, + VOLUME = {28}, + NUMBER = {8}, + PAGES = {1464--1472}, + ANNOTE = {} + } + +@ARTICLE {reggio_etal_92, + AUTHOR = {Reggio, M. and Trepanier, J. Y. and Camarero, R.}, + TITLE = {Numerical simulation of the gas flow in a + circuit-breaker.}, + JOURNAL = ijnme, + YEAR = {1992}, + VOLUME = {34}, + NUMBER = {2}, + PAGES = {607--618}, + ANNOTE = {* unstructured adaptive grid with moving boundaries} + } + +@TECHREPORT {riley_deJarnette_90, + AUTHOR = {Riley, C. J. and DeJarnette, F. R}, + TITLE = {An approximate method for calculating three-dimensional + inviscid hypersonic flow fields.}, + INSTITUTION = {}, + YEAR = {1990}, + TYPE = nasatp, + NUMBER = {3018}, + ADDRESS = {}, + ANNOTE = {} + } + +@INPROCEEDINGS {roe_87, + AUTHOR = {Roe, P. L.}, + TITLE = {Finite-volume methods for the compressible + {Navier}-{Stokes} equations.}, + BOOKTITLE = {Numerical Methods is Laminar and Turbulent Flow. + Volume 5, Part 2.}, + YEAR = {1987}, + PAGES = {2088}, + PUBLISHER = {Pineridge Press}, + ANNOTE = {} + } + +@TECHREPORT {rogers_weidner_88, + AUTHOR = {Rogers, R. C. and Weidner, E. H.}, + TITLE = { Numerical analysis of the transient flow + from a shock tunnel facility. }, + INSTITUTION = {}, + YEAR = {1988}, + TYPE = {AIAA Paper}, + NUMBER = {88-3261}, + ADDRESS = {}, + ANNOTE = {} + } + +@INPROCEEDINGS {rogers_weidner_83, + AUTHOR = {Rogers, R. C. and Weidner, E. H.}, + TITLE = { Numerical predictions of residence time behind + a rearward-facing step with transverse injection. }, + BOOKTITLE = { 20th JANNAF Combustion Meeting. }, + YEAR = {1983}, + ANNOTE = {} + } + +@TECHREPORT {rudy_etal_89, + AUTHOR = {Rudy, D. H. and Kumar, A. and Gnoffo, P. A. and + Chakravarthy, S. R.}, + TITLE = {A validation study of four {Navier}-{Stokes} codes + for high-speed flows.}, + INSTITUTION = {}, + YEAR = {1989}, + TYPE = {AIAA Paper}, + NUMBER = {89-1838}, + ADDRESS = {}, + ANNOTE = {* test cases from Holden_78 high Mach number data + * wedge induced separation + * shock wave - boundary layer separation + * The three upwind codes all closely agree while + the finite-difference code has problems after shock + impingement + } + } + +@ARTICLE {rusanov_??, + AUTHOR = {Rusanov, V. V.}, + TITLE = {A blunt body in a supersonic stream.}, + JOURNAL = {Annual Review of Fluid Mechanics}, + YEAR = {}, + VOLUME = {8}, + NUMBER = {}, + PAGES = {377--404}, + ANNOTE = {} + } + +@TECHREPORT {ryan_etal_89, + AUTHOR = {Ryan, J. S. and Flores, J. and Chow, C. -Y.}, + TITLE = {Development and validation of {CNS} ({Compressible} + {Navier}-{Stokes}) for hypersonic applications.}, + INSTITUTION = {}, + YEAR = {1989}, + TYPE = {AIAA Paper}, + NUMBER = {89-1839}, + ADDRESS = {}, + ANNOTE = {* defines a Y+ and suggests a value of 0.2 for + adequate resolution + * NOTE the definition for Y+ incorrectly includes a_infinity + * Zonal approach with different equations in different + zones + } + } + +@ARTICLE {ryan_etal_90, + AUTHOR = {Ryan, J. S. and Flores, J. and Chow, C. -Y.}, + TITLE = {Development and validation of a {Navier}-{Stokes} + code for hypersonic external flow.}, + JOURNAL = aiaajsr, + YEAR = {1990}, + VOLUME = {27}, + NUMBER = {2}, + PAGES = {160--166}, + ANNOTE = {* updated version of AIAA-89-1839} + } + +-ss- + +@ARTICLE {sanders_92, + AUTHOR = {Sanders, R.}, + TITLE = {A staggered mesh finite difference scheme for the + computation of compressible flows.}, + JOURNAL = ijnme, + YEAR = {1992}, + VOLUME = {34}, + NUMBER = {2}, + PAGES = {507--517}, + ANNOTE = {* something different for shock capturing} + } + +@ARTICLE {selmin_formaggia_92, + AUTHOR = {Selmin, V. and Formaggia, L.}, + TITLE = {Simulation of hypersonic flows on unstructured grids.}, + JOURNAL = ijnme, + YEAR = {1992}, + VOLUME = {34}, + NUMBER = {2}, + PAGES = {569--606}, + ANNOTE = {* unstructured, adaptive grids} + } + +@ARTICLE {sinha_etal_71, + AUTHOR = {Sinha, R and Zakkay, V. and Erdos, J.}, + TITLE = {Flowfield analysis of plumes of two-dimensional + underexpanded jets by a time-dependent method.}, + JOURNAL = aiaaj, + YEAR = {1971}, + VOLUME = {9}, + NUMBER = {12}, + PAGES = {2363--2370}, + ANNOTE = {} + } + +@ARTICLE {smarr_etal_84, + AUTHOR = {Smarr, L. L. and Norman, M. L. and Winkler, K-H. A.}, + TITLE = {Shocks, interfaces, and petterns in supersonic jets.}, + JOURNAL = {Physica D}, + YEAR = {1984}, + VOLUME = {12}, + NUMBER = {}, + PAGES = {83--106}, + ANNOTE = {* upwinding code} + } + +@ARTICLE {so_zhang_91a, + AUTHOR = {So, R. M. C. and Zhang, H. S.}, + TITLE = {Flux-coordinate splitting technique for the + {Navier}-{Stokes} equations.}, + JOURNAL = aiaaj, + YEAR = {1991}, + VOLUME = {29}, + NUMBER = {9}, + PAGES = {1418--1425}, + ANNOTE = {} + } + +@ARTICLE {sod_78, + AUTHOR = {Sod, G. A.}, + TITLE = {A survey of several finite difference methods for + systems of nonlinear hyperbolic conservation laws.}, + JOURNAL = jcp, + YEAR = {1978}, + VOLUME = {27}, + NUMBER = {1}, + PAGES = {1--31}, + ANNOTE = {* this seems to be the start of the famous 1D + shock tube TEST CASE + } + } + +@INPROCEEDINGS {sod_87, + AUTHOR = {Sod, G. A.}, + TITLE = {A random vortex method for compressible turbulent flows.}, + BOOKTITLE = {Numerical Methods is Laminar and Turbulent Flow. + Volume 5, Part 2.}, + YEAR = {1987}, + PAGES = {2075}, + PUBLISHER = {Pineridge Press}, + ANNOTE = {} + } + +@ARTICLE {stolcis_johnson_90a, + AUTHOR = {Stolcis, L. and Johnson. L. J.}, + TITLE = {Solution of the {Euler} equations on unstructured + grids for two-dimensional flow.}, + JOURNAL = taj, + YEAR = {1990}, + VOLUME = {June/July}, + NUMBER = {}, + PAGES = {181--195}, + ANNOTE = {} + } + +@INPROCEEDINGS {stolcis_johnston_90b, + AUTHOR = {Stolcis, L. and Johnston, L. J.}, + TITLE = {Implementation of a high resolution {TVD} scheme for + compressible inviscid flow on unstructured grids.}, + BOOKTITLE = {12th International Conference on Numerical Methods + in Fluid Dynamics}, + YEAR = {1990}, + PAGES = {}, + PUBLISHER = {}, + ANNOTE = {} + } + +@INPROCEEDINGS {stolcis_johnston_87, + AUTHOR = {Stolcis, L. and Johnston, L. J.}, + TITLE = {Compressible flow calculations using a two-equation + turbulence model and unstructured grids.}, + BOOKTITLE = {Numerical Methods is Laminar and Turbulent Flow. + Volume 7, Part 2.}, + YEAR = {1991}, + PAGES = {922--932}, + PUBLISHER = {Pineridge Press}, + ANNOTE = {} + } + +@TECHREPORT {stoufflet_etal_87, + AUTHOR = {Stoufflet, B. and Periaux, J. and Fezoui, F. and + Dervieux, A.}, + TITLE = {Numerical simulation of {3-D} hypersonic {Euler} flows + around space vehicles using adapted finite elements.}, + INSTITUTION = {}, + YEAR = {1987}, + TYPE = {AIAA Paper}, + NUMBER = {87-0560}, + ADDRESS = {}, + ANNOTE = {} + } + +@TECHREPORT {sullins_etal_82, + AUTHOR = {Sullins, G. A. and Anderson, J. D. and Drummond, J. P.}, + TITLE = {Numerical investigation of supersonic base flow with + parallel injection.}, + INSTITUTION = {}, + YEAR = {1982}, + TYPE = {AIAA Paper}, + NUMBER = {82-1001}, + ADDRESS = {}, + ANNOTE = {} + } + +@TECHREPORT {swanson_turkel_85, + AUTHOR = {Swanson, R. C. and Turkel, E.}, + TITLE = {A multistage time-stepping scheme for the + {Navier}-{Stokes} equations.}, + INSTITUTION = {}, + YEAR = {1990}, + TYPE = {ICASE Report}, + NUMBER = {84-62}, + ADDRESS = {}, + ANNOTE = {* also AIAA Paper 85-0035} + } + +@INPROCEEDINGS {swanson_etal_91, + AUTHOR = {Swanson, R. C. and Turkel, E. and White, J. A.}, + TITLE = {An effective multigrid method for high-speed flows.}, + BOOKTITLE = {Fifth Copper Mountain Conference on Multigrid + Methods}, + YEAR = {1991}, + PAGES = {}, + PUBLISHER = {}, + ANNOTE = {* viscous limit on the time stepping} + } + +@ARTICLE {swanson_etal_92, + AUTHOR = {Swanson, R. C. and Turkel, E. and White, J. A.}, + TITLE = {An effective multigrid method for high-speed flows.}, + JOURNAL = {Communications in Applied Numerical Methods}, + YEAR = {1992}, + VOLUME = {8}, + NUMBER = {9}, + PAGES = {671--681}, + ANNOTE = {} + } + +@ARTICLE {swanson_turkel_92, + AUTHOR = {Swanson, R. C. and Turkel, E.}, + TITLE = {On central-difference and upwind schemes.}, + JOURNAL = jcp, + YEAR = {1992}, + VOLUME = {101}, + NUMBER = {}, + PAGES = {292--306}, + ANNOTE = {} + } + +-tt- + +@ARTICLE {takayama_inoue_91, + AUTHOR = { Takayama, K. and Inoue, O. }, + TITLE = { Shock wave diffraction over a 90 degree sharp corner - + posters presented at the 18th {ISSW}. }, + JOURNAL = { Shock Waves }, + YEAR = {1991}, + VOLUME = {1}, + NUMBER = {301--312}, + PAGES = {}, + ANNOTE = {} + } + +@ARTICLE {thomas_etal_72, + AUTHOR = {Thomas, P. D. and Vinokur, M. and Bastianon, R. and + Conti, R. J.}, + TITLE = {Numerical solution for the three-dimensional hypersonic + flow field of a blunt delta body.}, + JOURNAL = aiaaj, + YEAR = {1972}, + VOLUME = {10}, + NUMBER = {}, + PAGES = {887--894}, + ANNOTE = {Transformations used in the SPARK computations.} + } + +@INPROCEEDINGS {thomas_91, + AUTHOR = {Thomas, J. L.}, + TITLE = {An implicit multigrid scheme for hypersonic + strong-interaction flowfields.}, + BOOKTITLE = {Fifth Copper Mountain Conference on Multigrid + Methods}, + YEAR = {1991}, + PAGES = {}, + PUBLISHER = {}, + ANNOTE = {} + } + +@ARTICLE {thomas_92, + AUTHOR = {Thomas, J. L.}, + TITLE = {An implicit multigrid scheme for hypersonic + strong-interaction flowfields.}, + JOURNAL = {Communications in Applied Numerical Methods}, + YEAR = {1992}, + VOLUME = {8}, + NUMBER = {9}, + PAGES = {683--693}, + ANNOTE = {} + } + +@ARTICLE {thompson_87, + AUTHOR = {Thompson, K. W.}, + TITLE = {Time dependent boundary conditions for hyperbolic + systems.}, + JOURNAL = jcp, + YEAR = {1987}, + VOLUME = {68}, + NUMBER = {}, + PAGES = {1--24}, + ANNOTE = {} + } + +@ARTICLE {thompson_90, + AUTHOR = {Thompson, K. W.}, + TITLE = {Time-dependent boundary conditions for hyperbolic + systems, II.}, + JOURNAL = jcp, + YEAR = {1990}, + VOLUME = {89}, + NUMBER = {2}, + PAGES = {439--461}, + ANNOTE = {* general formalism that covers all cases} + } + +@ARTICLE {trepanier_etal_93, + AUTHOR = { Trepanier, J. Y. and Reggio, M. and Paraschivoiu, M. + and Camarero, R. }, + TITLE = { Unsteady {Euler} solutions for arbitrarily moving + bodies and boundaries. }, + JOURNAL = aiaaj, + YEAR = { 1993 }, + VOLUME = { 31 }, + NUMBER = { 10 }, + PAGES = { 1869 }, + ANNOTE = {} + } + +@TECHREPORT {turkel_etal_91, + AUTHOR = {Turkel, E. and Swanson, R. C. and Vasta, V. N. and + White, J. A.}, + TITLE = {Multigrid for hypersonic viscous two- and + three-dimensional flows.}, + INSTITUTION = {}, + YEAR = {1991}, + TYPE = {AIAA Paper}, + NUMBER = {91-1572}, + ADDRESS = {}, + ANNOTE = {} + } + +@ARTICLE {tworzydlo_etal_92b, + AUTHOR = {Tworzydlo, W. W. and Huang, C. Y. and Oden, J. T.}, + TITLE = {Adaptive implicit/explicit finite element methods for + axisymmetric viscous turbulent flows with moving boundaries.}, + JOURNAL = cmame, + YEAR = {1992}, + VOLUME = {97}, + NUMBER = {2}, + PAGES = {245--288}, + ANNOTE = {} + } + +@ARTICLE {tworzydlo_etal_92a, + AUTHOR = {Tworzydlo, W. W. and Oden, J. T. and Thornton, E. A.}, + TITLE = {Adaptive implicit/explicit finite element method for + compressible viscous flows.}, + JOURNAL = cmame, + YEAR = {1992}, + VOLUME = {95}, + NUMBER = {}, + PAGES = {397--440}, + ANNOTE = {} + } + +-uu- + +@INPROCEEDINGS {uchiyama_inoue_93, + AUTHOR = { Uchiyama, N. and Inoue, O. }, + TITLE = { Adaptive mesh refinement computation of compressible flow. }, + BOOKTITLE = { 19th ISSW, Marseille. }, + YEAR = {1993}, + PAGES = {}, + PUBLISHER = {}, + ANNOTE = {* diffracting shock problem } + } + +@ARTICLE {uchiyama_inoue_92, + AUTHOR = { Uchiyama, N. and Inoue, O. }, + TITLE = { On the performance of adaptive mesh refinement computation. }, + JOURNAL = { Shock Waves }, + YEAR = {1992}, + VOLUME = {2}, + NUMBER = {}, + PAGES = {117--120}, + ANNOTE = {* diffracting shock problem } + } + +-vv- + +@TECHREPORT {venkatakrishnan_mavriplis_91, + AUTHOR = {Venkatakrishnan, V. and Mavriplis, D. J.}, + TITLE = {Implicit solvers for unstructured meshes.}, + INSTITUTION = {}, + YEAR = {1991}, + TYPE = {ICASE Report}, + NUMBER = {91-40}, + ADDRESS = {}, + ANNOTE = {} + } + +@ARTICLE {vilsmeier_hanel_93, + AUTHOR = { Vilsmeier, R. and Hanel, D. }, + TITLE = { Adaptive methods on unstructured grids for {Euler} + and {Navier}-{Stokes} equations. }, + JOURNAL = caf, + YEAR = {1993}, + VOLUME = {22}, + NUMBER = {4/5}, + PAGES = {485--499}, + ANNOTE = {} + } + +@ARTICLE {volpe_93, + AUTHOR = {Volpe, G.}, + TITLE = {Performance of compressible flow codes at low {Mach} + numbers.}, + JOURNAL = aiaaj, + YEAR = {1993}, + VOLUME = {31}, + NUMBER = {1}, + PAGES = {49--56}, + ANNOTE = {} + } + +@ARTICLE {vonneumann_richtmyer_50, + AUTHOR = {Von Neumann, J. and Richtmyer, R. D.}, + TITLE = {A method for the numerical calculation of hydrodynamic + shocks.}, + JOURNAL = {Journal of Applied Physics}, + YEAR = {1950}, + VOLUME = {21}, + NUMBER = {}, + PAGES = {232--237}, + ANNOTE = {* the original paper on artificial dissipation} + } + +@INPROCEEDINGS {vos_bergman_90, + AUTHOR = {Vos, J. B. and Bergman, C. M.}, + TITLE = {The development of a multi-block flow solver for + parallel computers.}, + BOOKTITLE = {Supercomputing}, + YEAR = {1990}, + PAGES = {521--532}, + PUBLISHER = {}, + ANNOTE = {* explicit time-stepping -- commumication between + blocks + } + } + +@INPROCEEDINGS {vos_bergman_91, + AUTHOR = {Vos, J. B. and Bergman, C. M.}, + TITLE = {A multiblock flow solver for inviscid hypersonic flows.}, + BOOKTITLE = {Aerothermodynamics for Space Vehicles. SP-318.}, + YEAR = {1991}, + PAGES = {109--114}, + PUBLISHER = {European Space Agency}, + ANNOTE = {} + } + +-ww- + +@ARTICLE {wang_widhopf_90, + AUTHOR = {Wang, J. C. T. and Widhopf, G. F.}, + TITLE = {Numerical simulation of blast flowfields using a high + resolution {TVD} finite volume scheme.}, + JOURNAL = caf, + YEAR = {1990}, + VOLUME = {18}, + NUMBER = {1}, + PAGES = {103-137}, + ANNOTE = {* extensive experimental verification + * axisymmetric flows} + } + +@INPROCEEDINGS {wanie_schmatz_91, + AUTHOR = {Wanie, K. M. and Schmatz, M. A.}, + TITLE = {Verification and application of the {NSFLEX} method for + hypersonic flow conditions.}, + BOOKTITLE = {Aerothermodynamics for Space Vehicles. SP-318.}, + YEAR = {1991}, + PAGES = {249--257}, + PUBLISHER = {European Space Agency}, + ANNOTE = {* multiblock flow solver} + } + +@INPROCEEDINGS {winzell_91, + AUTHOR = {Winzell, B.}, + TITLE = {Validation of a computational method for laminar + hypersonic flow around blunt bodies and the application + to the full {Hermes} spacecraft.}, + BOOKTITLE = {Aerothermodynamics for Space Vehicles. SP-318.}, + YEAR = {1991}, + PAGES = {51--59}, + PUBLISHER = {European Space Agency}, + ANNOTE = {} + } + +-xx- +-yy- + +@ARTICLE {yabe_etal_91, + AUTHOR = {Yabe, T. and Aoki, T. and Sakaguchi, G. and + Wang, P. -Y. and Ishikawa, T.}, + TITLE = {The compact {CIP} (Cubic-interpolated pseudo-particle) + method as a general hyperbolic solver.}, + JOURNAL = caf, + YEAR = {1991}, + VOLUME = {19}, + NUMBER = {3/4}, + PAGES = {421--431}, + ANNOTE = {} + } + +@INPROCEEDINGS {yadlin_etal_91, + AUTHOR = {Yadlin, Y. and Tysinger, T. L. and Caughey, D. A.}, + TITLE = {Parallel block multigrid solution of the compressible + {Navier}-{Stokes} equations.}, + BOOKTITLE = {AIAA 10th Computational Fluid Dynamics Conference}, + YEAR = {1991}, + PAGES = {965--966}, + PUBLISHER = {}, + ANNOTE = {* multiblock grid} + } + +@INPROCEEDINGS {yamamoto_etal_87, + AUTHOR = {Yamamoto, M. and Hatakeyama, M. and Oguchi, H.}, + TITLE = {Shock-tube flow simulation by a modified finite volume + method.}, + BOOKTITLE = {Shock Tubes and Waves.}, + YEAR = {1987}, + PAGES = {725--731}, + PUBLISHER = {}, + ANNOTE = {* forward facing step problem with experimental data} + } + +@ARTICLE {yang_etal_87, + AUTHOR = {Yang, J. Y. and Lombard, C. K. and Bershader, D.}, + TITLE = {Numerical simulation of transient inviscid shock tube + flows.}, + JOURNAL = aiaaj, + YEAR = {1987}, + VOLUME = {25}, + NUMBER = {2}, + PAGES = {245--251}, + ANNOTE = {* upwind scheme - TVD + * one dimensional shock tube problem + * two dimensional shock tube flows over a circular arc aerofoil + and a shock running up a ramp} + } + +@INPROCEEDINGS {yang_etal_90, + AUTHOR = {Yang, J. Y. and Hsu, C. -A. and Lee, T. H.}, + TITLE = {A numerical study of third-order nonoscillatory + schemes for the {Euler} equations.}, + BOOKTITLE = {12th International Conference on Numerical Methods + in Fluid Dynamics}, + YEAR = {1990}, + PAGES = {}, + PUBLISHER = {}, + ANNOTE = {* look to have a very nice shock tunnel nozzle starting + simulation + * contoured nozzle, large Mach number ?? + * perfect gas, 2-dimensional? + } + } + +@ARTICLE {yang_hsu_92, + AUTHOR = {Yang, J. Y. and Hsu, C. A.}, + TITLE = {High-resolution, nonoscillatory schemes for unsteady + compressible flows.}, + JOURNAL = aiaaj, + YEAR = {1992}, + VOLUME = {30}, + NUMBER = {6}, + PAGES = {1570--1575}, + ANNOTE = {* journal article from yang_etal_90 + * flow over an elliptic cylinder + * starting flow through a nozzle + } + } + +@ARTICLE {yang_etal_93, + AUTHOR = {Yang, J. Y. and Hsu, C. A. and Hui, W. H.}, + TITLE = {Solution of steady {Euler} equations in a generalized + {Lagrangian} formulation.}, + JOURNAL = aiaaj, + YEAR = {1993}, + VOLUME = {31}, + NUMBER = {2}, + PAGES = {266--272}, + ANNOTE = {} + } + +@TECHREPORT {yungster_91, + AUTHOR = {Yungster, S.}, + TITLE = {Numerical study of shock-wave/boundary layer interactions + in premixed hydrogen-air hypersonic flows.}, + INSTITUTION = {}, + YEAR = {1991}, + TYPE = {AIAA Paper}, + NUMBER = {91-0413}, + ADDRESS = {}, + ANNOTE = {* used laminar data from skebe_etal_87 as a + test case for the high Mach number calculations + } + } + +-zz- + +@ARTICLE {zhang_so_90, + AUTHOR = {Zhang, H. S. and So, R. M. C.}, + TITLE = {Calculation of the material interface in a pressure-wave + supercharger.}, + JOURNAL = {Proceedings of the Institute of Mechanical Engineers}, + YEAR = {1990}, + VOLUME = {204}, + NUMBER = {}, + PAGES = {151--161}, + ANNOTE = {} + } + +@ARTICLE {zhang_so_91a, + AUTHOR = {Zhang, H. S. and So, R. M. C.}, + TITLE = {A flux-coordinate-splitting technique for flows with + shocks and contact discontinuities.}, + JOURNAL = {Computers and Fluids}, + YEAR = {1991}, + VOLUME = {20}, + NUMBER = {4}, + PAGES = {421--442}, + ANNOTE = {} + } + +@ARTICLE {zhang_zhuang_92, + AUTHOR = {Zhang, H. and Zhuang, F.}, + TITLE = {{NND} schemes and their applications to numerical + simulation of two- and three-dimensional flows.}, + JOURNAL = {Advances in Applied Mechanics}, + YEAR = {1992}, + VOLUME = {29}, + NUMBER = {}, + PAGES = {193--256}, + ANNOTE = {* non-oscillatory schemes for the N-S equations + * uses third-order viscous terms with no adjustable parameters + } + }
--- a/examples/eilmer3/user-guide/bibtex/gas_dynamic.bib Mon May 26 12:01:15 2014 +1000 +++ b/examples/eilmer3/user-guide/bibtex/gas_dynamic.bib Mon May 26 12:30:16 2014 +1000 @@ -1031,6 +1031,59 @@ ANNOTE = {} } +@TECHREPORT { huber_1963a, + AUTHOR = { Huber, Paul W. }, + TITLE = { Hypersonic shock-heated flow parameters for velocities to 46000 ft/s + and altitudes to 323000 feet. }, + INSTITUTION = { NASA }, + ADDRESS = {}, + YEAR = { 1963 }, + MONTH = { December }, + TYPE = { Technical Report }, + NUMBER = { R-163 }, + ANNOTE = { * validation data for real air normal-shock processing } + } + +@TECHREPORT { hudgins_1965a, + AUTHOR = { Hudgins, H. E. }, + TITLE = { Supersonic flow about right circular cones at zero yaw in air + at chemical equilibrium. Part {I} Correlation of flow properties. }, + INSTITUTION = { Picatinny Arsenal }, + ADDRESS = { Dover, New Jersey }, + YEAR = { 1965 }, + MONTH = {}, + TYPE = { Technical Memorandum }, + NUMBER = { 1493 }, + ANNOTE = {} + } + +@TECHREPORT { hudgins_1964a, + AUTHOR = { Hudgins, H. E. }, + TITLE = { Supersonic flow about right circular cones at zero yaw in air + at chemical equilibrium. Parts {II} and {III} Tables of data. }, + INSTITUTION = { Picatinny Arsenal }, + ADDRESS = { Dover, New Jersey }, + YEAR = { 1964 }, + MONTH = { September }, + TYPE = { Technical Memorandum }, + NUMBER = { 1493 }, + ANNOTE = {} + } + +@TECHREPORT { hunt_souders_1975a, + AUTHOR = { Hunt, James L. and Souders, Sue W. }, + TITLE = { Normal- and oblique-shock flow parameters in equilibrium air + including attached-shock solutions for surfaces at angle of + attack, sweep and dihedral. }, + INSTITUTION = { NASA }, + ADDRESS = {}, + YEAR = { 1975 }, + MONTH = {}, + TYPE = { Special Publication }, + NUMBER = { NASA-SP-3093 }, + ANNOTE = { * validation data for oblique shock processing } + } + -ii- @ARTICLE { igra_etal_94, @@ -1533,6 +1586,17 @@ ANNOTE = {} } +@ARTICLE { mohammadian_1972a, + AUTHOR = { Mohammadian, S. }, + TITLE = { Viscous interaction over convave and convex surfaces at hypersonic speeds. }, + JOURNAL = jfm, + YEAR = { 1972 }, + VOLUME = { 55 }, + NUMBER = { 1 }, + PAGES = { 163--175 }, + ANNOTE = {} + } + @ARTICLE {morduchow_libby_49, AUTHOR = {Morduchow, M. and Libby, P. A.}, TITLE = {On a complete solution of the one-dimensional flow
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/examples/eilmer3/user-guide/cubic-ramp.tex Mon May 26 12:30:16 2014 +1000 @@ -0,0 +1,181 @@ +% cubic-ramp.tex + +\section{Hypersonic flow over a concave surface.} +\label{sec:cubic-ramp} +% +This is one of the two hypersonic flows studied by Mohammadian\,\cite{mohammadian_1972a} +in the Imperial College gun tunnel, more than 4 decades ago. +The gun tunnel was operated with a total pressure of 1600\,psia (11.03\,MPa) and +a total temperature of 1300\,K with a Mach 12.25 contoured nozzle. + +\medskip +Since we don't have full information on the tunnel and its operating condition, +we have to make a few assumptions. +First, we assume that the nozzle produced a parallel and uniform flow of ideal air +with free stream conditions $p$ = 63.43\,Pa, $T$=41.92\,K and $u$ = 1.59\,km/s. +Using Sutherland's expression for the viscosity of air, +we estimate the viscosity of the free stream to be $\mu = 2.593 \times 10^{-6}$\,Pa.s. +Taking a length scale $L = 1$\,inch, we compute a Reynolds number $Re_L = 0.86 \times 10^{5}$, +which is the same as that reported in the original paper\,\cite{mohammadian_1972a}. + +\bigskip +\subsection{Input script (.py)} +% +Figure\,\ref{fig:cubic-ramp-geometry} shows the flow region, as modelled for simulation. +The region is very simple but we have divided it into 22 blocks so that the computational load +can be shared across a number of CPU cores. + +\begin{figure}[htbp] + \centering + \includegraphics[width=\textwidth,viewport=0 0 520 214,clip=true]{../2D/cubic-ramp/cubic-ramp-edited.pdf} + \caption{Schematic view of the simulated flow region for the hypersonic flow + over Mohammadian's concave ramp.} + \label{fig:cubic-ramp-geometry} +\end{figure} + +\medskip +The concave ramp is defined by +$$ +y = \frac{1}{150} \, x^3 +$$ +where $x$ is in inches and the surface angle is less than 28$^o$. +Beyond that point, the ramp surface is assumed straight until the corner +at $x$ = 6.4\,inches. +The ramp surface temperature was assumed to be a constant 296\,K. + +\noindent +\topbar +\lstinputlisting[language={}]{../2D/cubic-ramp/cubic-ramp.py} +\bottombar + + +\bigskip +\subsection{Running the simulation} +% +In terms of required computer time, this simulation is fairly demanding, +taking more than 12 hours on a 4-core workstation. +The job scipts submitted to the batch system are shown below. +Note that the preparation script sets up the mapping of the full set of 22 blocks to fit onto 4 MPI tasks. + +\noindent +\topbar +\lstinputlisting[language={}]{../2D/cubic-ramp/prep.sh}\index{mpimap!example of use} +\bottombar\\ +\topbar +\lstinputlisting[language={}]{../2D/cubic-ramp/run.sh} +\bottombar\\ + +\subsection{Results} +% +Figure\,\ref{fig:cubic-ramp-field-data} shows some of the flow field data +at $t$=1\,ms after flow start. +This is sufficient time for the flow to reach steady state. + +\begin{figure}[htbp] + \centering + \subfloat[Pressure field.]{\includegraphics[width=0.7\textwidth] + {../2D/cubic-ramp/cubic-ramp-factor-2-log10p-field-1-ms.png}\label{fig:cubic-ramp-pressure}}\\ + \subfloat[Temperature field.]{\includegraphics[width=0.7\textwidth] + {../2D/cubic-ramp/cubic-ramp-factor-2-T-field-1-ms.png}\label{fig:cubic-ramp-temperature}}\\ + \subfloat[Mach number.]{\includegraphics[width=0.7\textwidth] + {../2D/cubic-ramp/cubic-ramp-factor-2-M-field-1-ms.png}\label{fig:cubic-ramp-mach}} + \caption{Computed flow field at $t$=1\,ms.} + \label{fig:cubic-ramp-field-data} +\end{figure} + +\medskip +The logarithmic pressure field shows the leading-edge interaction shock propagating into the free-stream +flow but then intersecting the ramp about two-thirds of the way along its length. +The gradually increasing pressure can also be seen in the near-surface region, leading up to this intersection. + +\medskip +The temperature field shows more clearly the boundary layer that grows along the concave surface. +It also shows the compression of the boundary-layer flow as the surface curves up. +The oblique shock propagating up over the top of the ramp is a combination of the reflected lead-edge +interaction shock and the coalesced compression waves from the curved ramp. + +\clearpage + +\medskip +Although the computed flow field looks plausible, +the real proof of success of the simulation is in comparison with the experimental data. +Figure\,\ref{fig:cubic-ramp-data-compare} shows the pressure and heat-transfer +along the surface of the ramp. +The simulation has done a good job of estimating the pressure distribution for the early part of the ramp, +and does a fair job all the way up to the sharp corner at the top of the ramp, +although there appears to be a mismatch in the location of this corner +(indicated by the sharp drop in pressure at the right end of each data set). + +\medskip +The simulation has also done a good job on the heat transfer estimate, +which has been computed from the field data using the script in Section\,\ref{cubic-ramp-post-processing}. +Mohammadian has not provided dimensional data in the original paper so we have normalized the simulation +data is the same way as can be best guessed (with the assistance of Andrew Knisely, University of Illinois). +First, we compute local heat transfer from the normal gradient of temperature at the ramp surface, +followed by Stanton number as +$$ +St = \frac{q}{\rho U C_p (T_0 - T_w)} +$$ +and then plot the combination $St . Re_x^{\frac{1}{2}}$, to remove the singularity in heat transfer +at the leading edge of the ramp. +Agreement for the early part of the plate to 110\,mm is excellent, so we can have some +confidence in the codes ability to model hypersonic viscous interactions, however, +what happens beyond that point is not captured by this purely two-dimensional simulation. + +\begin{figure}[htbp] + \centering + \subfloat[Pressure.]{\includegraphics[width=0.5\textwidth] + {../2D/cubic-ramp/surface-pressure.pdf}\label{fig:cubic-ramp-surface-pressure}} + \subfloat[Heat transfer.]{\includegraphics[width=0.5\textwidth] + {../2D/cubic-ramp/surface-heat-transfer.pdf}\label{fig:cubic-ramp-heat-transfer}} + \caption{Distribution of pressure and heat transfer along the concave ramp. + Simulation data is recorded at $t$=1\,ms into the simulation. + Experimental data is from Ref.\,\cite{mohammadian_1972a}.} + \label{fig:cubic-ramp-data-compare} +\end{figure} + +\medskip +The boundary-layer thickness, as identified by the outer edge of the maximum density gradient +seen in a schlieren image was also provided by Mohammadian. +Figure\,\ref{fig:cubic-ramp-grad-rho-field} shows the density gradient field of the simulated +flow and, from this image, corresponding points were measured manually +(with the assistance of the \verb!g3data! program). +These boundary-layer thickness data are shown in Figure\,\ref{fig:cubic-ramp-delta-star}, +together with the experimental values from Ref.\cite{mohammadian_1972a}. +Although there is some scatter in the simulation-derived data, comparison is good. + +\begin{figure}[htb] + \centering + \includegraphics[width=0.7\textwidth]{../2D/cubic-ramp/cubic-ramp-factor-2-grad-rho-field-1-ms-zoom-with-scale.png} + \caption{Computed density gradient field.} + \label{fig:cubic-ramp-grad-rho-field} +\end{figure} + +\begin{figure}[htb] + \centering + \includegraphics[width=0.7\textwidth]{../2D/cubic-ramp/delta-star.pdf} + \caption{Estimates of the boundary-layer displacement thickness along the ramp.} + \label{fig:cubic-ramp-delta-star} +\end{figure} + + +\bigskip +\subsection{Postprocessing to get heat transfer} +\label{cubic-ramp-post-processing} +% +The scripts below use the functions imported from \verb!e3_flow.py! +at a slightly higher level than in the cone20 example. +The first extracts the data for the cell nearest to the ramp surface +and uses that data to compute the expected shear stress and heat transfer at the surface. + +\noindent +\topbar +\lstinputlisting[language={}]{../2D/cubic-ramp/surface_properties.py} +\bottombar + +\subsection{Notes} +\begin{itemize} + \item Plotting was done with the following GNUPlot scripts. + \lstinputlisting[language={}]{../2D/cubic-ramp/surface-pressure.gnuplot} + \lstinputlisting[language={}]{../2D/cubic-ramp/surface-heat-transfer.gnuplot} +\end{itemize}
--- a/examples/eilmer3/user-guide/eilmer3-user-guide.tex Mon May 26 12:01:15 2014 +1000 +++ b/examples/eilmer3/user-guide/eilmer3-user-guide.tex Mon May 26 12:30:16 2014 +1000 @@ -230,6 +230,10 @@ \cleardoublepage \include{axi-cylinder} \cleardoublepage +\include{cubic-ramp} +%\cleardoublepage +%\include{convex-ramp} +\cleardoublepage \include{cylinder-flare} \cleardoublepage \include{double-cone-sharp-nose}