--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/examples/eilmer3/2D/nenzfr-UQ-T4-M7-nozzle/nenzfr-UQ-T4-M7-nozzle-eq-block-marching.cfg	Mon Mar 02 20:50:58 2020 +1000
@@ -0,0 +1,159 @@
+# ------------------------ Initial setup ------------------------------------
+# This is where the intital settings such as the facility and gas parameters are set
+
+# Facility that is being simulated.
+# This is where the facility being simulated can be chosen. 
+# There are three types of facilities, each with their own parameters:
+#   -reflected shock tunnels ('reflected-shock-tunnel')
+#   -gun tunnels ('gun-tunnel')    
+#   -expansion tubes ('expansion-tube')
+
+facility = 'reflected-shock-tunnel'
+
+# Gas model to be used.
+# Currently there are five different gas models that can be selected:
+#   -air ('air')
+#   -5 species air ('air')
+#   -nitrogen ('n2')
+#   -carbon dioxide ('co2')
+#   -H2/Ne ('h2ne')
+
+gasName = 'air'
+
+# Chemistry model to be used.
+# Currently there are four different chemistry models that can be selected:
+#   -equilibrium ('eq')
+#   -non-equilibrium ('neq')
+#   -frozen ('frz')
+#   -frozen2 ('frz2') (Details about the differences are explained in the nenzfr manual.)
+
+chemModel = 'eq'
+
+# Flow conditions
+# These conditions are dependant on the facility being simulated.
+# reflected shock tunnel simulations require:
+#   -T1: ambient temperature in the shock tube, in degrees K
+#   -p1: fill pressure in the shock tube, in Pa
+#   -Vs: shock speed through the shock tube, in m/s
+#   -pe: equilibrium pressure (after shock reflection), in Pa
+# gun tunnel simulations require:
+#   -T0: stagnation temperature, in degrees K
+#   -p0: stagnation pressure, in Pa
+# expansion tube facilities require:
+#   -T7: unsteadility expanded test gas temperature, in degrees K
+#   -p7: unsteadily expanded test gas pressure, in Pa
+#   -V7: unsteadily expanded test gas velocity, in m/s
+
+T1 = 300.0
+p1 = 131.0e3
+Vs = 1644.0
+pe = 8.32e6
+
+# Nozzle area ratio
+# This is only used for the estcj calculation and should be used
+# when a contour of gride file are specified.
+
+areaRatio = 27.0
+
+# ------------------------- Eilmer 3 setup ----------------------------------
+# All of the parameters required to get eilmer 3 up and running.
+
+# Eilmer 3 job title.
+
+jobName = 'nozzle'
+
+# Nozzle to use.
+# This can be one of the default nozzles (currently: 't4-m4', 't4-m6', 't4-m7',
+# 't4-m8b', 't4-m10b', 'x2-m10', 'x3-m10') or a custom nozzle name (in which
+# case you MUST also define either contourFileName or gridFileName)
+
+nozzle = 't4-m7'
+
+# Contour file.
+# file containing Bezier control points for nozzle contour
+
+#contourFileName = 'Bezier-control-pts-t4-m7.data'
+
+# Grid file
+# file containing the nozzle grid. This will be ignored if either a default
+# nozzle name or a contour file name are specified.
+
+#gridFileName = 'None'
+
+# Exit file
+# File for holding the nozzle exit data.
+# Will be set to 'nozzle-exit.data' if not specified.
+
+exitSliceFileName = 'nozzle-exit.data'
+
+# Exit-flow statistics output.
+# If turned on, program will skip the detailed calculations and 
+# just retrieve exit-flow statistics.
+
+justStats = False
+
+# Flag to switch off exit-flow statistic calculations
+# If turned on, nenzfr will skip the exit-flow statistic calculations.
+#
+#noStats = False
+
+# Block marching switch
+# If turned on, nenzfr will run in block marching mode.
+
+blockMarching = True
+
+# Number of cells in the axial and radial directions.
+# Variable nni is number of axial cells, and variable nnj is number of radial cells.
+# Must be an integer.
+
+nni = 600
+nnj = 80
+
+# Number of axial and radial blocks for the divergence section (nozzle_blk).
+# Variable nbi is axial blocks, nbj is radial blocks.
+# Must be an integer.
+
+nbi = 30
+nbj = 4
+
+# Everything below here is commented out so the default values in the program are used
+# (Any value that has been commented out is the default value from the program.)
+
+# Clustering in the axial and radial directions.
+# Variable bx is axial clustering, variable by is radial clustering.
+
+bx = 1.5
+by = 1.002
+
+# Maximum time.
+# Overall simulation time for nozzle flow.
+
+max_time = 2.0e-3
+
+# Maximum steps.
+# Maximum number of simulation steps allowed.
+
+max_step = 1000000
+
+# Nozzle wall temperature, in degrees K.
+
+#Tw = 300.0
+
+# Transition location for the boundary layer.
+# Used to define the turbulent portion of the nozzle.
+
+#BLTrans = "x_c[-1]*1.1"
+
+# Turbulent to Laminar Viscosity Ratio.
+
+#TurbVisRatio = 100.0
+
+# Turbulence intensity at the throat.
+
+#TurbInten = 0.05
+
+# Radius of core flow as a fraction of the nozzle exit radius.
+
+#coreRfraction = 2.0/3.0
+
+

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/examples/eilmer3/2D/nenzfr-UQ-T4-M7-nozzle/nozzle-centreline.data	Mon Mar 02 20:50:58 2020 +1000
@@ -0,0 +1,611 @@
+# Variables: 1:pos.x 2:pos.y 3:pos.z 4:volume 5:rho 6:vel.x 7:vel.y 8:vel.z 9:p 10:a 11:mu 12:k[0] 13:mu_t 14:k_t 15:S 16:tke 17:omega 18:massf[0]-LUT 19:e[0] 20:T[0] 21:M_local 22:pitot_p 23:total_p 24:total_h
+ -1.010939e-02 6.801736e-04 0.000000e+00 2.403482e-10 8.579482e+00 8.229373e+02 -8.476118e-02 0.000000e+00 4.594106e+06 8.296544e+02 6.633896e-05 1.140720e-01 0.000000e+00 0.000000e+00 0.000000e+00 2.576112e+03 3.311972e+06 1.000000e+00 1.566603e+06 1.865494e+03 9.919037e-01 8.302004e+06 8.302004e+06 2.443268e+06
+ -9.250393e-03 6.801736e-04 0.000000e+00 2.882087e-10 8.588529e+00 8.221465e+02 -1.036097e-01 0.000000e+00 4.600296e+06 8.297669e+02 6.635201e-05 1.141049e-01 0.000000e+00 0.000000e+00 0.000000e+00 2.576112e+03 3.311972e+06 1.000000e+00 1.567152e+06 1.866040e+03 9.908162e-01 8.303017e+06 8.303017e+06 2.443323e+06
+ -8.241401e-03 6.801736e-04 0.000000e+00 3.326416e-10 8.579409e+00 8.230502e+02 -8.853604e-02 0.000000e+00 4.594011e+06 8.296498e+02 6.633842e-05 1.140706e-01 0.000000e+00 0.000000e+00 0.000000e+00 2.576112e+03 3.311972e+06 1.000000e+00 1.566580e+06 1.865471e+03 9.920454e-01 8.303151e+06 8.303151e+06 2.443332e+06
+ -7.103701e-03 6.801736e-04 0.000000e+00 3.674058e-10 8.566821e+00 8.242397e+02 -9.664348e-02 0.000000e+00 4.585342e+06 8.294881e+02 6.631967e-05 1.140233e-01 0.000000e+00 0.000000e+00 0.000000e+00 2.576112e+03 3.311972e+06 1.000000e+00 1.565792e+06 1.864687e+03 9.936727e-01 8.302694e+06 8.302694e+06 2.443298e+06
+ -5.878301e-03 6.801736e-04 0.000000e+00 3.866044e-10 8.564071e+00 8.246061e+02 -1.021041e-01 0.000000e+00 4.583444e+06 8.294524e+02 6.631554e-05 1.140129e-01 0.000000e+00 0.000000e+00 0.000000e+00 2.576112e+03 3.311972e+06 1.000000e+00 1.565618e+06 1.864514e+03 9.941572e-01 8.303786e+06 8.303786e+06 2.443376e+06
+ -4.621699e-03 6.801736e-04 0.000000e+00 3.866044e-10 8.564149e+00 8.246331e+02 -9.669879e-02 0.000000e+00 4.583493e+06 8.294530e+02 6.631561e-05 1.140131e-01 0.000000e+00 0.000000e+00 0.000000e+00 2.576112e+03 3.311972e+06 1.000000e+00 1.565621e+06 1.864517e+03 9.941890e-01 8.304171e+06 8.304171e+06 2.443402e+06
+ -3.396299e-03 6.801736e-04 0.000000e+00 3.674058e-10 8.563623e+00 8.247129e+02 -8.910576e-02 0.000000e+00 4.583128e+06 8.294460e+02 6.631479e-05 1.140110e-01 0.000000e+00 0.000000e+00 0.000000e+00 2.576112e+03 3.311972e+06 1.000000e+00 1.565587e+06 1.864483e+03 9.942937e-01 8.304487e+06 8.304487e+06 2.443424e+06
+ -2.258599e-03 6.801736e-04 0.000000e+00 3.326416e-10 8.562603e+00 8.248291e+02 -7.458072e-02 0.000000e+00 4.582426e+06 8.294329e+02 6.631327e-05 1.140072e-01 0.000000e+00 0.000000e+00 0.000000e+00 2.576112e+03 3.311972e+06 1.000000e+00 1.565523e+06 1.864419e+03 9.944495e-01 8.304673e+06 8.304673e+06 2.443438e+06
+ -1.249607e-03 6.801736e-04 0.000000e+00 2.882087e-10 8.565248e+00 8.245865e+02 -8.426096e-02 0.000000e+00 4.584237e+06 8.294660e+02 6.631712e-05 1.140169e-01 0.000000e+00 0.000000e+00 0.000000e+00 2.576112e+03 3.311972e+06 1.000000e+00 1.565684e+06 1.864580e+03 9.941173e-01 8.304841e+06 8.304841e+06 2.443446e+06
+ -3.906084e-04 6.801736e-04 0.000000e+00 2.403482e-10 8.563021e+00 8.248592e+02 -1.404135e-01 0.000000e+00 4.582668e+06 8.294344e+02 6.631345e-05 1.140076e-01 0.000000e+00 0.000000e+00 0.000000e+00 2.576021e+03 3.311884e+06 1.000000e+00 1.565531e+06 1.864427e+03 9.944840e-01 8.305432e+06 8.305432e+06 2.443473e+06
+ 1.359277e-04 6.802373e-04 0.000000e+00 8.365181e-11 8.468548e+00 8.341388e+02 -2.308373e-01 0.000000e+00 4.517775e+06 8.282174e+02 6.617262e-05 1.136522e-01 6.496977e-03 9.058963e+00 0.000000e+00 2.425026e+03 3.161003e+06 1.000000e+00 1.559609e+06 1.858529e+03 1.007150e+00 8.306212e+06 8.306216e+06 2.443405e+06
+ 4.113657e-04 6.804933e-04 0.000000e+00 8.592132e-11 8.434235e+00 8.376491e+02 -1.847569e-01 0.000000e+00 4.494230e+06 8.277701e+02 6.612098e-05 1.135218e-01 6.348309e-03 8.850642e+00 0.000000e+00 2.226702e+03 2.958416e+06 1.000000e+00 1.557438e+06 1.856365e+03 1.011935e+00 8.308134e+06 8.308153e+06 2.443348e+06
+ 6.939342e-04 6.810059e-04 0.000000e+00 8.823941e-11 8.410469e+00 8.401028e+02 -1.406855e-01 0.000000e+00 4.477945e+06 8.274599e+02 6.608520e-05 1.134315e-01 6.209305e-03 8.656151e+00 0.000000e+00 2.039824e+03 2.762985e+06 1.000000e+00 1.555933e+06 1.854864e+03 1.015279e+00 8.309748e+06 8.309786e+06 2.443284e+06
+ 9.835678e-04 6.817739e-04 0.000000e+00 9.061288e-11 8.389802e+00 8.422318e+02 -9.516251e-02 0.000000e+00 4.463789e+06 8.271890e+02 6.605398e-05 1.133527e-01 6.080365e-03 8.475806e+00 0.000000e+00 1.874556e+03 2.586596e+06 1.000000e+00 1.554620e+06 1.853555e+03 1.018185e+00 8.311107e+06 8.311170e+06 2.443221e+06
+ 1.280208e-03 6.827958e-04 0.000000e+00 9.304843e-11 8.365272e+00 8.447205e+02 -2.545683e-02 0.000000e+00 4.446996e+06 8.268663e+02 6.601683e-05 1.132589e-01 5.954860e-03 8.300163e+00 0.000000e+00 1.728059e+03 2.427588e+06 1.000000e+00 1.553058e+06 1.851997e+03 1.021593e+00 8.312293e+06 8.312398e+06 2.443165e+06
+ 1.583801e-03 6.840706e-04 0.000000e+00 9.555266e-11 8.331735e+00 8.480728e+02 8.917569e-02 0.000000e+00 4.424057e+06 8.264237e+02 6.596591e-05 1.131303e-01 5.827686e-03 8.121972e+00 0.000000e+00 1.597111e+03 2.283399e+06 1.000000e+00 1.550917e+06 1.849860e+03 1.026196e+00 8.313348e+06 8.313535e+06 2.443117e+06
+ 1.894303e-03 6.855967e-04 0.000000e+00 9.813210e-11 8.285560e+00 8.526384e+02 2.599734e-01 0.000000e+00 4.392517e+06 8.258115e+02 6.589558e-05 1.129527e-01 5.695578e-03 7.936600e+00 0.000000e+00 1.479279e+03 2.151996e+06 1.000000e+00 1.547960e+06 1.846906e+03 1.032486e+00 8.314237e+06 8.314589e+06 2.443077e+06
+ 2.211671e-03 6.873728e-04 0.000000e+00 1.007932e-10 8.224946e+00 8.585855e+02 4.947804e-01 0.000000e+00 4.351187e+06 8.250028e+02 6.580288e-05 1.127185e-01 5.557107e-03 7.742031e+00 0.000000e+00 1.372746e+03 2.031804e+06 1.000000e+00 1.544062e+06 1.843011e+03 1.040706e+00 8.314859e+06 8.315542e+06 2.443043e+06
+ 2.535872e-03 6.893976e-04 0.000000e+00 1.035425e-10 8.149837e+00 8.659159e+02 7.941156e-01 0.000000e+00 4.300089e+06 8.239929e+02 6.568737e-05 1.124266e-01 5.412551e-03 7.538680e+00 0.000000e+00 1.276198e+03 1.921639e+06 1.000000e+00 1.539206e+06 1.838152e+03 1.050878e+00 8.315104e+06 8.316413e+06 2.443016e+06
+ 2.866876e-03 6.916697e-04 0.000000e+00 1.063863e-10 8.061595e+00 8.744813e+02 1.173452e+00 0.000000e+00 4.240247e+06 8.227988e+02 6.554792e-05 1.120834e-01 5.263165e-03 7.328183e+00 0.000000e+00 1.188507e+03 1.820467e+06 1.000000e+00 1.533460e+06 1.832411e+03 1.062814e+00 8.314673e+06 8.317086e+06 2.442989e+06
+ 3.204657e-03 6.941876e-04 0.000000e+00 1.093312e-10 7.959693e+00 8.843331e+02 1.667161e+00 0.000000e+00 4.171392e+06 8.214085e+02 6.538239e-05 1.116863e-01 5.108614e-03 7.110054e+00 0.000000e+00 1.108561e+03 1.727268e+06 1.000000e+00 1.526769e+06 1.825731e+03 1.076608e+00 8.313352e+06 8.317625e+06 2.442966e+06
+ 3.549197e-03 6.969498e-04 0.000000e+00 1.123835e-10 7.843424e+00 8.955366e+02 2.280277e+00 0.000000e+00 4.093113e+06 8.198001e+02 6.519170e-05 1.112286e-01 4.948491e-03 6.883916e+00 0.000000e+00 1.035403e+03 1.641154e+06 1.000000e+00 1.519061e+06 1.818023e+03 1.092388e+00 8.310730e+06 8.318025e+06 2.442944e+06
+ 3.900479e-03 6.999549e-04 0.000000e+00 1.155498e-10 7.713038e+00 9.080645e+02 3.013252e+00 0.000000e+00 4.005695e+06 8.179678e+02 6.497549e-05 1.107097e-01 4.783207e-03 6.650392e+00 0.000000e+00 9.682854e+02 1.561408e+06 1.000000e+00 1.510321e+06 1.809268e+03 1.110153e+00 8.306284e+06 8.318277e+06 2.442925e+06
+ 4.258492e-03 7.032014e-04 0.000000e+00 1.188367e-10 7.569815e+00 9.217946e+02 3.846787e+00 0.000000e+00 3.910119e+06 8.159188e+02 6.473500e-05 1.101324e-01 4.613886e-03 6.411115e+00 0.000000e+00 9.065812e+02 1.487414e+06 1.000000e+00 1.500599e+06 1.799511e+03 1.129773e+00 8.299410e+06 8.318383e+06 2.442907e+06
+ 4.623229e-03 7.066878e-04 0.000000e+00 1.222507e-10 7.416229e+00 9.364917e+02 4.714789e+00 0.000000e+00 3.808164e+06 8.136784e+02 6.447363e-05 1.095052e-01 4.442706e-03 6.169216e+00 0.000000e+00 8.498976e+02 1.418760e+06 1.000000e+00 1.490032e+06 1.788882e+03 1.150950e+00 8.289493e+06 8.318320e+06 2.442892e+06
+ 4.994686e-03 7.104126e-04 0.000000e+00 1.257987e-10 7.257627e+00 9.516543e+02 5.503760e+00 0.000000e+00 3.703461e+06 8.113152e+02 6.419963e-05 1.088475e-01 4.273572e-03 5.930280e+00 0.000000e+00 7.979269e+02 1.355107e+06 1.000000e+00 1.478955e+06 1.777714e+03 1.172997e+00 8.276262e+06 8.318112e+06 2.442877e+06
+ 5.372864e-03 7.143741e-04 0.000000e+00 1.294874e-10 7.098745e+00 9.668374e+02 6.028944e+00 0.000000e+00 3.599195e+06 8.088966e+02 6.392102e-05 1.081785e-01 4.110031e-03 5.699356e+00 0.000000e+00 7.504912e+02 1.296250e+06 1.000000e+00 1.467693e+06 1.766331e+03 1.195278e+00 8.259682e+06 8.317741e+06 2.442867e+06
+ 5.757766e-03 7.185708e-04 0.000000e+00 1.333238e-10 6.949140e+00 9.811417e+02 6.146887e+00 0.000000e+00 3.501577e+06 8.065685e+02 6.365456e-05 1.075386e-01 3.958501e-03 5.485561e+00 0.000000e+00 7.075296e+02 1.242085e+06 1.000000e+00 1.456922e+06 1.755419e+03 1.216463e+00 8.240836e+06 8.317279e+06 2.442854e+06
+ 6.149399e-03 7.230011e-04 0.000000e+00 1.373150e-10 6.808979e+00 9.945568e+02 6.277890e+00 0.000000e+00 3.410625e+06 8.043409e+02 6.340116e-05 1.069299e-01 3.818405e-03 5.288054e+00 0.000000e+00 6.685053e+02 1.192095e+06 1.000000e+00 1.446679e+06 1.745018e+03 1.236511e+00 8.220181e+06 8.316774e+06 2.442840e+06
+ 6.547772e-03 7.276634e-04 0.000000e+00 1.414681e-10 6.675378e+00 1.007364e+03 6.538723e+00 0.000000e+00 3.324393e+06 8.021742e+02 6.315613e-05 1.063411e-01 3.687131e-03 5.103110e+00 0.000000e+00 6.328214e+02 1.145709e+06 1.000000e+00 1.436774e+06 1.734940e+03 1.255818e+00 8.197672e+06 8.316255e+06 2.442827e+06
+ 6.952898e-03 7.325560e-04 0.000000e+00 1.457907e-10 6.543582e+00 1.020018e+03 7.040604e+00 0.000000e+00 3.239775e+06 7.999935e+02 6.291096e-05 1.057519e-01 3.560536e-03 4.924861e+00 0.000000e+00 5.996612e+02 1.102080e+06 1.000000e+00 1.426865e+06 1.724834e+03 1.275063e+00 8.172607e+06 8.315667e+06 2.442815e+06
+ 7.364794e-03 7.376773e-04 0.000000e+00 1.502901e-10 6.409686e+00 1.032906e+03 7.854876e+00 0.000000e+00 3.154273e+06 7.977321e+02 6.265823e-05 1.051443e-01 3.436089e-03 4.749707e+00 0.000000e+00 5.688561e+02 1.061162e+06 1.000000e+00 1.416650e+06 1.714395e+03 1.294841e+00 8.144190e+06 8.315086e+06 2.442808e+06
+ 7.783477e-03 7.430256e-04 0.000000e+00 1.549741e-10 6.268247e+00 1.046541e+03 9.020707e+00 0.000000e+00 3.064511e+06 7.952994e+02 6.238276e-05 1.044942e-01 3.309721e-03 4.571714e+00 0.000000e+00 5.397365e+02 1.022218e+06 1.000000e+00 1.405694e+06 1.703192e+03 1.315957e+00 8.110573e+06 8.314185e+06 2.442792e+06
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+ 9.989886e-01 8.847357e-03 0.000000e+00 1.053000e-07 2.208005e-02 2.106767e+03 1.738700e-01 0.000000e+00 1.407518e+03 2.988207e+02 1.469626e-05 2.039718e-02 1.227741e-06 1.384163e-03 0.000000e+00 1.052361e+00 1.892607e+04 1.000000e+00 1.596378e+05 2.221238e+02 7.050272e+00 9.076881e+04 6.065223e+06 2.442619e+06

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/examples/eilmer3/2D/nenzfr-UQ-T4-M7-nozzle/nozzle-exit.data	Mon Mar 02 20:50:58 2020 +1000
@@ -0,0 +1,81 @@
+# Variables: 1:pos.x 2:pos.y 3:pos.z 4:volume 5:rho 6:vel.x 7:vel.y 8:vel.z 9:p 10:a 11:mu 12:k[0] 13:mu_t 14:k_t 15:S 16:tke 17:omega 18:massf[0]-LUT 19:e[0] 20:T[0] 21:M_local 22:pitot_p 23:total_p 24:total_h
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+ 9.969670e-01 8.846676e-03 0.000000e+00 1.051424e-07 2.208196e-02 2.106764e+03 2.158799e-01 0.000000e+00 1.407688e+03 2.988258e+02 1.469663e-05 2.039772e-02 1.228574e-06 1.385102e-03 0.000000e+00 1.055180e+00 1.896554e+04 1.000000e+00 1.596432e+05 2.221313e+02 7.050140e+00 9.077641e+04 6.065252e+06 2.442619e+06
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+ 9.969090e-01 1.361644e-01 0.000000e+00 1.635735e-08 1.156916e-02 6.923790e+02 3.966449e+00 0.000000e+00 1.767656e+03 4.596662e+02 2.832005e-05 4.068580e-02 5.656136e-05 6.588744e-02 0.000000e+00 1.154954e+04 2.362346e+06 1.000000e+00 3.850598e+05 5.322248e+02 1.506290e+00 6.030705e+03 6.504528e+03 7.891019e+05
+ 9.969090e-01 1.362202e-01 0.000000e+00 1.501656e-08 1.172589e-02 6.477163e+02 3.737862e+00 0.000000e+00 1.775850e+03 4.577110e+02 2.813422e-05 4.040493e-02 4.322024e-05 5.030829e-02 0.000000e+00 1.035293e+04 2.808790e+06 1.000000e+00 3.815975e+05 5.275520e+02 1.415144e+00 5.471183e+03 5.735056e+03 7.531725e+05
+ 9.969090e-01 1.362714e-01 0.000000e+00 1.378473e-08 1.194261e-02 5.988759e+02 3.492430e+00 0.000000e+00 1.785546e+03 4.548757e+02 2.786648e-05 4.000028e-02 3.160953e-05 3.675310e-02 0.000000e+00 8.951363e+03 3.381956e+06 1.000000e+00 3.766091e+05 5.208162e+02 1.316593e+00 4.909186e+03 5.028649e+03 7.144033e+05
+ 9.969089e-01 1.363184e-01 0.000000e+00 1.265314e-08 1.223853e-02 5.450465e+02 3.225715e+00 0.000000e+00 1.796884e+03 4.509047e+02 2.749498e-05 3.943879e-02 2.173507e-05 2.523336e-02 0.000000e+00 7.348031e+03 4.137492e+06 1.000000e+00 3.696873e+05 5.114628e+02 1.208805e+00 4.346981e+03 4.382535e+03 6.724002e+05
+ 9.969089e-01 1.363615e-01 0.000000e+00 1.161377e-08 1.264008e-02 4.854216e+02 2.927820e+00 0.000000e+00 1.809764e+03 4.454562e+02 2.699180e-05 3.867827e-02 1.365456e-05 1.581954e-02 0.000000e+00 5.588982e+03 5.173719e+06 1.000000e+00 3.603121e+05 4.987812e+02 1.089738e+00 3.793693e+03 3.796698e+03 6.268991e+05
+ 9.969088e-01 1.364011e-01 0.000000e+00 1.065921e-08 1.318185e-02 4.195056e+02 2.583699e+00 0.000000e+00 1.823544e+03 4.381034e+02 2.632464e-05 3.766993e-02 7.482487e-06 8.645072e-03 0.000000e+00 3.797597e+03 6.690170e+06 1.000000e+00 3.478819e+05 4.819445e+02 9.575674e-01 3.274916e+03 3.274916e+03 5.780127e+05
+ 9.969088e-01 1.364374e-01 0.000000e+00 9.782624e-09 1.390449e-02 3.476922e+02 2.179025e+00 0.000000e+00 1.836643e+03 4.283981e+02 2.546474e-05 3.637027e-02 3.324747e-06 3.827703e-03 0.000000e+00 2.190340e+03 9.160206e+06 1.000000e+00 3.318604e+05 4.602053e+02 8.116260e-01 2.824993e+03 2.824993e+03 5.265879e+05
+ 9.969088e-01 1.364707e-01 0.000000e+00 8.977726e-09 1.485412e-02 2.717781e+02 1.742757e+00 0.000000e+00 1.847105e+03 4.160150e+02 2.440133e-05 3.476303e-02 1.073517e-06 1.230478e-03 0.000000e+00 1.003317e+03 1.388269e+07 1.000000e+00 3.120472e+05 4.332614e+02 6.533026e-01 2.456814e+03 2.456814e+03 4.743333e+05
+ 9.969088e-01 1.365012e-01 0.000000e+00 8.238713e-09 1.607742e-02 1.944496e+02 1.328108e+00 0.000000e+00 1.852463e+03 4.008503e+02 2.314969e-05 3.287128e-02 2.119576e-07 2.416882e-04 0.000000e+00 3.301627e+02 2.504348e+07 1.000000e+00 2.887267e+05 4.014630e+02 4.851041e-01 2.174736e+03 2.174736e+03 4.231845e+05
+ 9.969087e-01 1.365293e-01 0.000000e+00 7.560248e-09 1.768844e-02 1.177184e+02 1.095970e+00 0.000000e+00 1.855372e+03 3.827876e+02 2.163685e-05 3.060609e-02 1.813856e-08 2.058759e-05 0.000000e+00 6.209498e+01 6.055367e+07 1.000000e+00 2.625421e+05 3.654602e+02 3.075425e-01 1.980868e+03 1.980868e+03 3.744254e+05
+ 9.969087e-01 1.365550e-01 0.000000e+00 6.937414e-09 2.004839e-02 3.879333e+01 2.485171e-01 0.000000e+00 1.856804e+03 3.598304e+02 1.956614e-05 2.756028e-02 1.803072e-10 2.042451e-07 0.000000e+00 3.609800e+00 3.650105e+08 1.000000e+00 2.318408e+05 3.226834e+02 1.078123e-01 1.871934e+03 1.871934e+03 3.252130e+05

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/examples/eilmer3/2D/nenzfr-UQ-T4-M7-nozzle/nozzle-exit.stats	Mon Mar 02 20:50:58 2020 +1000
@@ -0,0 +1,21 @@
+  variable    mean-value        minus        plus    std-dev
+------------------------------------------------------------
+       rho       0.02244     -0.000401   0.000507   0.000307
+     vel.x          2106         -0.97      0.788       0.58
+     vel.y       -0.0905         -3.96       5.02        3.3
+         p          1440           -37       45.9       27.6
+         a         299.8         -1.18       1.35      0.818
+        mu     1.477e-05     -8.53e-08   9.84e-08   5.94e-08
+      k[0]       0.02051     -0.000125   0.000145   8.73e-05
+      mu_t      1.22e-06     -3.59e-08   4.16e-08   2.83e-08
+       k_t      0.001375     -4.06e-05    4.7e-05   3.19e-05
+       tke        0.9897       -0.0505     0.0832     0.0474
+     omega      1.82e+04          -618        882        544
+massf[0]-LUT             1             0          0          0
+      e[0]     1.607e+05     -1.26e+03   1.46e+03        880
+      T[0]         223.7         -1.76       2.03       1.23
+   M_local         7.024       -0.0348     0.0303     0.0211
+   pitot_p     9.218e+04     -1.59e+03   2.01e+03   1.21e+03
+   total_p     6.063e+06     -2.16e+04   6.35e+03   6.07e+03
+   total_h     2.443e+06          -118       22.1       31.7
+------------------------------------------------------------
\ No newline at end of file

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/examples/eilmer3/2D/nenzfr-UQ-T4-M7-nozzle/run-mpi-block-marching-mode.sh	Mon Mar 02 20:50:58 2020 +1000
@@ -0,0 +1,11 @@
+#! /bin/bash 
+# run-mpi-block-marching-mode.sh
+#
+# Running nenzfr using the new multi-process block-marching mode 
+# that has recently been implemented. Note the two new options
+# needed when running in this mode (nbj and blockMarching variables
+# that can be seen in the cfg file).
+
+echo "Start time: "; date
+nenzfr.py --config_file=nenzfr-UQ-T4-M7-nozzle-eq-block-marching.cfg  > LOGFILE
+echo "Finish time: "; date

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/examples/eilmer3/2D/nenzfr-optimisation-UQ-T4-M7-nozzle-eq/Bezier-control-pts-t4-m7.initial.data	Mon Mar 02 20:50:58 2020 +1000
@@ -0,0 +1,10 @@
+#     x, m       y, m 
+ 0.000000e+00 1.050000e-02
+ 3.000000e-02 1.050000e-02
+ 1.200000e-01 6.800000e-02
+ 1.600000e-01 5.010000e-02
+ 2.600000e-01 8.959000e-02
+ 4.000000e-01 1.088600e-01
+ 5.700000e-01 1.172100e-01
+ 7.700000e-01 1.349500e-01
+ 1.000000e+00 1.350300e-01

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/examples/eilmer3/2D/nenzfr-optimisation-UQ-T4-M7-nozzle-eq/analysis-scripts/generate-initial-contour.py	Mon Mar 02 20:50:58 2020 +1000
@@ -0,0 +1,58 @@
+#! /usr/bin/env python 
+# generate-initial-contour.py
+#
+# This script generates a file that contains x- and y-coordinates
+# of the initial (pre-optimised) contour of the nozzle. This file
+# is generated from the given Bezier control points.
+#
+# Wilson Chan, 30 Nov 2013.
+# ------------------------------------------------------------------
+
+from math import *
+
+def eval_Bezier(bezCtrlPts, t):
+    """
+    Return the x- and y-coordinates of point t (0 < t < 1) on
+    the Bezier curve generated by the input control points .
+    """
+    n = len(bezCtrlPts) - 1
+    blendingFunc = []
+    # Generate blending functions.
+    for i in range(len(bezCtrlPts)):
+        blendingFunc.append((factorial(n) /(factorial(i)*factorial(n-i))) *\
+            pow(t,i) * pow((1-t),(n-i)))
+    # Get x and y coordinates.
+    x = 0.0; y = 0.0
+    for i in range(len(bezCtrlPts)):
+        x += blendingFunc[i] * bezCtrlPts[i][0]
+        y += blendingFunc[i] * bezCtrlPts[i][1]
+    return x, y
+
+
+# ------------------------------------------------------------------
+
+nPtsOnCurve = 1000  # Number of points on curve generated by the Bezier points
+
+fo = open("contour-t4-m4.initial.data", "w")
+
+# Read in initial Bezier control points
+controlPts = []
+fi = open("../Bezier-control-pts-t4-m4.initial.data", "r")
+fi.readline()
+while True:
+    buf = fi.readline().strip()
+    if len(buf) == 0: break
+    buf_temp = buf.split()
+    if buf_temp[0] == "#": continue
+    tokens = [float(word) for word in buf.split()]
+    controlPts.append([tokens[0], tokens[1]])
+fi.close()
+
+# Generate data points for the Bezier curve
+for n in range(nPtsOnCurve+1):
+    t = float(n)/float(nPtsOnCurve)
+    x, y = eval_Bezier(controlPts, t)
+    fo.write("%.6e %.6e\n" % (x, y))
+fo.write("\n")
+fo.close()
+

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/examples/eilmer3/2D/nenzfr-optimisation-UQ-T4-M7-nozzle-eq/analysis-scripts/generate-optimised-curves-comparison.py	Mon Mar 02 20:50:58 2020 +1000
@@ -0,0 +1,97 @@
+#! /usr/bin/env python 
+# generate-optimised-curves-comparison.py
+#
+# Wilson Chan, 25 May 2012.
+# ------------------------------------------------------------------
+
+from math import *
+
+def eval_Bezier(bezCtrlPts, t):
+    """
+    Return the x- and y-coordinates of point t (0 < t < 1) on
+    the Bezier curve generated by the input control points .
+    """
+    n = len(bezCtrlPts) - 1
+    blendingFunc = []
+    # Generate blending functions.
+    for i in range(len(bezCtrlPts)):
+        blendingFunc.append((factorial(n) /(factorial(i)*factorial(n-i))) *\
+            pow(t,i) * pow((1-t),(n-i)))
+    # Get x and y coordinates.
+    x = 0.0; y = 0.0
+    for i in range(len(bezCtrlPts)):
+        x += blendingFunc[i] * bezCtrlPts[i][0]
+        y += blendingFunc[i] * bezCtrlPts[i][1]
+    return x, y
+
+
+# ------------------------------------------------------------------
+
+nPtsOnCurve = 1000  # Number of points on curve generated by the Bezier points
+
+nIter =  0
+n_checks = 5 # As per specified in optimisation script.
+
+fo = open("optimised-curves-comparison.data", "w")
+fo2 = open("residuals.data", "w")
+fo3 = open("optimised-curves-controlpts.data", "w")
+
+# Read in initial Bezier control points
+controlPts = []
+fi = open("../Bezier-control-pts-t4-m4.initial.data", "r")
+fi.readline()
+while True:
+    buf = fi.readline().strip()
+    if len(buf) == 0: break
+    tokens = [float(word) for word in buf.split()]
+    controlPts.append([tokens[0], tokens[1]])
+fi.close()
+    
+# Generate data points for the Bezier curve
+for n in range(nPtsOnCurve+1):
+    t = float(n)/float(nPtsOnCurve)
+    x, y = eval_Bezier(controlPts, t)
+    fo.write("%.6e %.6e\n" % (x, y))
+fo.write("\n")
+
+# Write out Bezier control points
+for n in range(len(controlPts)):
+    fo3.write("%.6e %.6e\n" % (controlPts[n][0], controlPts[n][1]))
+fo3.write("\n")
+
+# Read all optimised curves
+fi = open("../nelmin.log", "r")
+while True:
+    buf = fi.readline().strip()
+    if len(buf) == 0: break
+    tokens = [word for word in buf.split()]
+    if tokens[0] == "x":
+        # Generate control points.
+        for n in range(2, len(controlPts)):
+            if n == 2:
+                newY = controlPts[n-1][1] + float(tokens[n][1:9])
+            else:
+                newY = controlPts[n-1][1] + float(tokens[n][0:8])
+            controlPts[n][1] = newY
+        # Generate data points for the Bezier curve
+        for n in range(nPtsOnCurve+1):
+            t = float(n)/float(nPtsOnCurve)
+            x, y = eval_Bezier(controlPts, t)
+            fo.write("%.6e %.6e\n" % (x, y))
+        fo.write("\n")
+        # Write out Bezier control points
+        for n in range(len(controlPts)):
+            fo3.write("%.6e %.6e\n" % (controlPts[n][0], controlPts[n][1]))
+        fo3.write("\n")
+    # Write out optimisation statistics
+    if tokens[0] == "Number":
+        noFuncEvals = int(tokens[5])
+    if tokens[0] == "Current":
+        nIter += n_checks
+        fo2.write("%d %d %s\n" % (nIter, noFuncEvals, tokens[4]))
+
+fi.close()
+fo.close()
+fo2.close()
+fo3.close()
+

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/examples/eilmer3/2D/nenzfr-optimisation-UQ-T4-M7-nozzle-eq/analysis-scripts/plot-optimised-curves-comparison.sh	Mon Mar 02 20:50:58 2020 +1000
@@ -0,0 +1,36 @@
+#!/bin/sh
+# plot-optimised-curves-comparison.sh
+#
+
+./generate-initial-contour.py
+./generate-optimised-curves-comparison.py
+
+gnuplot<<EOF
+set term postscript eps color enhanced size 20cm,4cm
+set output "optimised-curves-comparison.eps"
+set key right center
+set xlabel "Axial distance, m"
+set ylabel "Radial distance, m"
+set size ratio -1
+
+plot "contour-t4-m4.initial.data" using (\$1):(\$2) title "Initial contour" with lines lt 1 lc 1, \
+     "optimised-curves-comparison.data" every :::0::0 using (\$1):(\$2) title "after 0-th optimisation run" with lines lt 1 lc 2, \
+     "" every :::5::5 using (\$1):(\$2) title "after 5-th optimisation run" with lines lt 1 lc 3, \
+     "" every :::10::10 using (\$1):(\$2) title "after 10-th optimisation run" with lines lt 1 lc 4, \
+     "" every :::12::12 using (\$1):(\$2) title "after 12-th optimisation run" with lines lt 1 lc 5, \
+     "" every :::14::14 using (\$1):(\$2) title "after 14-th optimisation run" with lines lt 1 lc 6
+EOF
+
+gnuplot<<EOF
+set term postscript eps color enhanced size 12cm,9cm
+set output "residuals.eps"
+set logscale y
+set xlabel "Number of iterations"
+set ylabel "Objective function value"
+unset key
+plot "residuals.data" using (\$1):(\$3) with linespoint lt 1 lc 1
+EOF
+
+epstopdf optimised-curves-comparison.eps
+epstopdf residuals.eps
+rm *eps

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/examples/eilmer3/2D/nenzfr-optimisation-UQ-T4-M7-nozzle-eq/nenzfr-UQ-T4-M7-nozzle-eq-block-marching.cfg	Mon Mar 02 20:50:58 2020 +1000
@@ -0,0 +1,159 @@
+# ------------------------ Initial setup ------------------------------------
+# This is where the intital settings such as the facility and gas parameters are set
+
+# Facility that is being simulated.
+# This is where the facility being simulated can be chosen. 
+# There are three types of facilities, each with their own parameters:
+#   -reflected shock tunnels ('reflected-shock-tunnel')
+#   -gun tunnels ('gun-tunnel')    
+#   -expansion tubes ('expansion-tube')
+
+facility = 'reflected-shock-tunnel'
+
+# Gas model to be used.
+# Currently there are five different gas models that can be selected:
+#   -air ('air')
+#   -5 species air ('air')
+#   -nitrogen ('n2')
+#   -carbon dioxide ('co2')
+#   -H2/Ne ('h2ne')
+
+gasName = 'air'
+
+# Chemistry model to be used.
+# Currently there are four different chemistry models that can be selected:
+#   -equilibrium ('eq')
+#   -non-equilibrium ('neq')
+#   -frozen ('frz')
+#   -frozen2 ('frz2') (Details about the differences are explained in the nenzfr manual.)
+
+chemModel = 'eq'
+
+# Flow conditions
+# These conditions are dependant on the facility being simulated.
+# reflected shock tunnel simulations require:
+#   -T1: ambient temperature in the shock tube, in degrees K
+#   -p1: fill pressure in the shock tube, in Pa
+#   -Vs: shock speed through the shock tube, in m/s
+#   -pe: equilibrium pressure (after shock reflection), in Pa
+# gun tunnel simulations require:
+#   -T0: stagnation temperature, in degrees K
+#   -p0: stagnation pressure, in Pa
+# expansion tube facilities require:
+#   -T7: unsteadility expanded test gas temperature, in degrees K
+#   -p7: unsteadily expanded test gas pressure, in Pa
+#   -V7: unsteadily expanded test gas velocity, in m/s
+
+T1 = 300.0
+p1 = 131.0e3
+Vs = 1644.0
+pe = 8.32e6
+
+# Nozzle area ratio
+# This is only used for the estcj calculation and should be used
+# when a contour of gride file are specified.
+
+areaRatio = 27.0
+
+# ------------------------- Eilmer 3 setup ----------------------------------
+# All of the parameters required to get eilmer 3 up and running.
+
+# Eilmer 3 job title.
+
+jobName = 'nozzle'
+
+# Nozzle to use.
+# This can be one of the default nozzles (currently: 't4-m4', 't4-m6', 't4-m7',
+# 't4-m8b', 't4-m10b', 'x2-m10', 'x3-m10') or a custom nozzle name (in which
+# case you MUST also define either contourFileName or gridFileName)
+
+#nozzle = 't4-m7'
+
+# Contour file.
+# file containing Bezier control points for nozzle contour
+
+contourFileName = 'Bezier-control-pts-t4-m7.initial.data'
+
+# Grid file
+# file containing the nozzle grid. This will be ignored if either a default
+# nozzle name or a contour file name are specified.
+
+#gridFileName = 'None'
+
+# Exit file
+# File for holding the nozzle exit data.
+# Will be set to 'nozzle-exit.data' if not specified.
+
+exitSliceFileName = 'nozzle-exit.data'
+
+# Exit-flow statistics output.
+# If turned on, program will skip the detailed calculations and 
+# just retrieve exit-flow statistics.
+
+justStats = False
+
+# Flag to switch off exit-flow statistic calculations
+# If turned on, nenzfr will skip the exit-flow statistic calculations.
+#
+#noStats = False
+
+# Block marching switch
+# If turned on, nenzfr will run in block marching mode.
+
+blockMarching = True
+
+# Number of cells in the axial and radial directions.
+# Variable nni is number of axial cells, and variable nnj is number of radial cells.
+# Must be an integer.
+
+nni = 300
+nnj = 40
+
+# Number of axial and radial blocks for the divergence section (nozzle_blk).
+# Variable nbi is axial blocks, nbj is radial blocks.
+# Must be an integer.
+
+nbi = 30
+nbj = 4
+
+# Everything below here is commented out so the default values in the program are used
+# (Any value that has been commented out is the default value from the program.)
+
+# Clustering in the axial and radial directions.
+# Variable bx is axial clustering, variable by is radial clustering.
+
+bx = 1.5
+by = 1.002
+
+# Maximum time.
+# Overall simulation time for nozzle flow.
+
+max_time = 2.0e-3
+
+# Maximum steps.
+# Maximum number of simulation steps allowed.
+
+max_step = 1000000
+
+# Nozzle wall temperature, in degrees K.
+
+#Tw = 300.0
+
+# Transition location for the boundary layer.
+# Used to define the turbulent portion of the nozzle.
+
+#BLTrans = "x_c[-1]*1.1"
+
+# Turbulent to Laminar Viscosity Ratio.
+
+#TurbVisRatio = 100.0
+
+# Turbulence intensity at the throat.
+
+#TurbInten = 0.05
+
+# Radius of core flow as a fraction of the nozzle exit radius.
+
+#coreRfraction = 2.0/3.0
+
+

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/examples/eilmer3/2D/nenzfr-optimisation-UQ-T4-M7-nozzle-eq/optimise_T4_Mach_7_nozzle.py	Mon Mar 02 20:50:58 2020 +1000
@@ -0,0 +1,188 @@
+#! /usr/bin/env python 
+# optimise_T4_Mach_7_nozzle.py
+#
+# This script optimises an initial contour for a supersonic nozzle 
+# using the design methodology suggested by Chris Craddock (UQ 
+# Mechanical Engineering Departmental Report 2/00). It uses the
+# minimize() function in cfcfd3/lib/cfpylib/nm/nelmin.py. 
+#
+# Wilson Chan, 26 May 2012.
+# ------------------------------------------------------------------
+
+import sys, os
+from math import tan, radians
+import shlex, subprocess
+from subprocess import PIPE
+sys.path.append(os.path.expandvars("$HOME/e3bin")) # installation directory
+sys.path.append("") # so that we can find user's scripts in current directory
+from cfpylib.nm.nelmin import *
+
+
+def run_command(cmdText):
+    """
+    Run the command as a subprocess.
+    """
+    print "About to run cmd:", cmdText
+    if (type(cmdText) is list):
+        args = cmdText
+    else:
+        args = shlex.split(cmdText)
+    p = subprocess.Popen(args)
+    # wait until the subprocess is finished
+    stdoutData, stderrData = p.communicate()
+    return
+
+
+def objective_function(y):
+    """
+    Objective function for the design of the internal contour of 
+    a T4 nozzle. The input y is a list of coordinates of the 
+    Bezier control points for the nozzle. The radial coordinates 
+    are specified relative to the radial coordinate of the 
+    upstream point.
+    """
+
+    nFixedPts = 2  # Number of fixed Bezier control points
+
+    # Targets
+    M_target = 7.0        # Target Mach number
+    dtheta_target = 0.02  # Target variation in outflow angle (in degrees)
+    dM_target = 0.01      # Target variation in Mach number
+
+    # Read in the x-coordinates for all points and the y-coordinates for
+    # the first nFixedPts points - they are fixed and not changed  in the 
+    # optimisation run.
+    x_fixed = []; y_fixed = []
+    fi = open('Bezier-control-pts-t4-m7.initial.data', 'r')
+    fi.readline()  # Skip the first line
+    while True:
+        buf = fi.readline().strip()
+        if len(buf) == 0: break
+        tokens = [float(word) for word in buf.split()]
+        x_fixed.append(tokens[0])
+        y_fixed.append(tokens[1])
+    fi.close()
+ 
+    # Use x and y to create new data file containing Bezier control
+    # points to generate the internal contour of the nozzle.
+    fo = open('Bezier-control-pts-t4-m7.data', 'w')
+    fo.write('#    x, m    y, m \n')
+    for indx in range(nFixedPts):
+        fo.write('%.7f %.7f \n' % (x_fixed[indx], y_fixed[indx]))
+    y_absolute = y_fixed[nFixedPts-1]
+    for indx in range(nFixedPts, len(y)+nFixedPts):
+        y_absolute += y[indx-nFixedPts]
+        fo.write('%.7f %.7f \n' % (x_fixed[indx], y_absolute))
+    fo.close()
+
+    # Run nenzfr with the given nozzle contour.
+    run_command('./run-mpi-block-marching-mode.sh')
+
+    # Read in an extracted slice of data at the exit of the nozzle
+    fi = open('nozzle-exit.data', 'r')
+    # Keep a list of variables in order of appearance (from nenzfr.py).
+    varLine = fi.readline().strip(); items = varLine.split()
+    if items[0] == '#': del items[0]
+    if items[0] == 'Variables:': del items[0]
+    variable_list = [item.split(':')[1] for item in items]
+    # Store the data in lists against these names (from nenzfr.py).
+    data = {}
+    for var in variable_list:
+        data[var] = []
+    for line in fi.readlines():
+        items = line.strip().split()
+        if items[0] == '#': continue
+        assert len(items) == len(variable_list)
+        for i in range(len(items)):
+            data[variable_list[i]].append(float(items[i]))    
+    fi.close()
+
+    # Secondary functions that contribute to the objective function.
+    f_theta = 0.0; f_M = 0.0 # Initialise both functions to zero first.
+    N = 0 # Initialise the counter for the number of cells in the boundary layer.
+    for j in range(len(data['pos.y'])):
+        # Definition used by Chris Craddock to estimate the boundary layer edge
+        # TODO -> I believe that we can improve this by looking at mu_t.
+        if j == 0: 
+            dMdy = 0.0  # Set to some number so that the first point 
+                        # is not set as the boundary layer edge.
+        else:
+            dMdy = (data['M_local'][j] - data['M_local'][j-1]) /\
+                   (data['pos.y'][j] - data['pos.y'][j-1])
+        # If dMdy >= -20.0, then we are in the core flow.
+        if dMdy >= -20.0:
+            f_theta += (data['vel.y'][j] / data['vel.x'][j])**2
+            f_M += (data['M_local'][j] - M_target)**2
+            N += 1
+
+    # Weighting parameters.
+    phi_theta = 1.0 / tan(radians(dtheta_target))
+    phi_M = 1.0 / dM_target
+
+    # Weight the secondary functions by weighting parameters.
+    f_theta = phi_theta**2 / N * f_theta
+    f_M = phi_M**2 / N * f_M
+
+    # Objective function
+    obj_funct = (f_theta + f_M)**2
+    return obj_funct
+
+
+def get_design_variables(filename, nFixedPts):
+    """
+    Generate the design variables from a given file. The other 
+    input is the number of fixed points in the data file that 
+    are not part of the list of design variables for the
+    optimisation run.
+
+    Returns a list of y-coordinates of the Bezier control points
+    that define the internal contour of a nozzle. Note that these
+    coordinates are relative to those of the upstream point.
+    """
+    y_absolute = []; y_relative = []
+    fi = open(filename, 'r')
+    fi.readline()  # Skip the first line
+    while True:
+        buf = fi.readline().strip()
+        if len(buf) == 0: break
+        tokens = [float(word) for word in buf.split()]
+        y_absolute.append(tokens[1])
+    fi.close()
+    for indx in range(nFixedPts, len(y_absolute)):
+        y_relative.append(y_absolute[indx] - y_absolute[indx-1])
+    return y_relative
+
+
+# ------------------------------------------------------------------
+
+if __name__ == '__main__':
+    print "Begin the optimisation of the T4 Mach 7 nozzle..."
+    print "---------------------------------------------------"
+    # List of N design variables 
+    x = get_design_variables('Bezier-control-pts-t4-m7.initial.data', 2)
+    # List of N increments to apply to x when 
+    # forming the initial simplex.
+    dx = [0.003, 0.003, 0.005, 0.005, 0.005, 0.005, 0.005]
+    #dx = [0.003, 0.003, 0.003, 0.005, 0.005, 0.005, 0.005, 0.005]
+    # Check that the sizes for the x and dx lists are the same.
+    if len(x) != len(dx):
+        print "Error! x and dx lists must have the same number of variables."
+        print "x has ", len(x), "variables, while dx has ", len(dx), "variables."
+        sys.exit()
+    # The terminating limit for the standard-deviation
+    # the simplex function values.
+    tol = 1.0
+    # Maximum number of function evaluations 
+    maxfe = 1000
+    # Number of steps between convergence checks
+    n_check = 5
+    # Start function minimisation
+    x, fx, conv_flag, nfe, nres = minimize(objective_function, x,
+                                           dx, tol, maxfe, n_check)
+    print "x = ", x
+    print "fx =", fx
+    print "convergence-flag =", conv_flag
+    print "number-of-fn-evaluations =", nfe
+    print "number-of-restarts =", nres
+    print "---------------------------------------------------"
+    print "Done."

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/examples/eilmer3/2D/nenzfr-optimisation-UQ-T4-M7-nozzle-eq/run-nenzfr-mpi-block-marching-mode.sh	Mon Mar 02 20:50:58 2020 +1000
@@ -0,0 +1,11 @@
+#! /bin/bash 
+# run-mpi-block-marching-mode.sh
+#
+# Running nenzfr using the new multi-process block-marching mode 
+# that has recently been implemented. Note the two new options
+# needed when running in this mode (nbj and blockMarching variables
+# that can be seen in the cfg file).
+
+echo "Start time: "; date
+nenzfr.py --config_file=nenzfr-UQ-T4-M7-nozzle-eq-block-marching.cfg  > LOGFILE
+echo "Finish time: "; date

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/examples/eilmer3/2D/nenzfr-optimisation-UQ-T4-M7-nozzle-eq/run-optimiser.sh	Mon Mar 02 20:50:58 2020 +1000
@@ -0,0 +1,6 @@
+#! /bin/bash 
+# run-optimiser.sh
+
+echo "Start time: "; date
+./optimise_T4_Mach_7_nozzle.py
+echo "Finish time: "; date