NOTE: This repository exists primarily as a submodule for the ElasticNozzleMDO 
problem. Stand-alone compilation and use of this solver is not supported, and 
may not work if attempted. For the coupled ElasticNozzleMDO problem, please 
refer to the repository at https://github.com/OptimalDesignLab/ElasticNozzleMDO

quasi_1d_euler is a CFD code for modelling simple nozzle flows.  The spatial
discretization uses summation-by-parts finite-difference operators and weakly
imposed boundary conditions.  The solution method is Newton-Krylov.

Dependencies

The code uses the Boost library.

Compiling

First, make sure the Kona directory is in your path.  For example, if you are
running the b`ash shell and you installed Kona in your home directory, you can
add the following line to your .bashrc file:

export LD_LIBRARY_PATH=/home/your_user_name/Kona:$LD_LIBRARY_PATH

Change to the test_solver directory and type make.  This should compile
solver.bin and verify.bin.  Run both of those executables.

Verification

The output from solver.bin should show the L2 norm of the residual decreasing
below 1E-10 in 7 iterations.  In addition, it should show the L2 and Lmax error
in the Mach nubmer being 2.69e-5 and 4.10e-5 (approximately).  Here is some
sample output:
------------------------------------------------------
iter = 0: L2 norm of residual = 0.1772
iter = 1: L2 norm of residual = 0.0185517
iter = 2: L2 norm of residual = 0.000828069
iter = 3: L2 norm of residual = 1.64644e-05
iter = 4: L2 norm of residual = 4.55325e-07
iter = 5: L2 norm of residual = 2.08853e-08
iter = 6: L2 norm of residual = 7.22471e-10
iter = 7: L2 norm of residual = 2.78434e-11
Quasi1DEuler: NewtonKrylov converged
L2 error in Mach number   = 2.69856e-05
Lmax error in Mach number = 4.09699e-05
------------------------------------------------------

The end of the output from verify.bin lists the truncation order of accuracy of
the "fourth-order" SBP operator.  The first 6 nodes (0 thru 5) and last 6 nodes
(35 thru 40) should have order = 3 (approximately) and the remaining interior
nodes should have orders of approximately 6.  Here is a sample output of those
orders:
------------------------------------------------------
node 0 order = 3.03077
node 1 order = 3.0154
node 2 order = 3.03022
node 3 order = 2.98882
node 4 order = 2.97356
node 5 order = 2.96023
node 6 order = 6.37174
node 7 order = 6.37174
node 8 order = 6.37174
node 9 order = 6.37174
node 10 order = 6.37174
node 11 order = 6.37174
node 12 order = 6.37174
node 13 order = 6.37174
node 14 order = 6.37174
node 15 order = 6.37174
node 16 order = 6.37174
node 17 order = 6.37174
node 18 order = 6.37174
node 19 order = 6.37174
node 20 order = 6.37174
node 21 order = 6.37174
node 22 order = 6.37174
node 23 order = 6.37174
node 24 order = 6.37174
node 25 order = 6.37174
node 26 order = 6.37174
node 27 order = 6.37174
node 28 order = 6.37174
node 29 order = 6.37174
node 30 order = 6.37174
node 31 order = 6.37174
node 32 order = 6.37174
node 33 order = 6.37174
node 34 order = 6.37174
node 35 order = 3.04019
node 36 order = 3.0269
node 37 order = 3.01155
node 38 order = 2.96842
node 39 order = 2.9849
node 40 order = 2.9696
------------------------------------------------------