grinsfem/grins — pull request #183 by tradowsk (2014-12-22 16:22:21+00:00)
Title: LowMachNavierStokes Jacobians from Master

This PR is a redo of #182, with the difference being that this PR has a target branch of `grinsfem/master`.

Implementation of analytical Jacobians for low_mach_navier_stokes.C based on residuals already implemented therein. Documentation of derivation will be added soon, once cleaned up and verified.

Created an example problem, cavity_benchmark_no_stab, to test in 3D. Tolerance for comparison between analytical and numerical Jacobians set to 5.0e-6, stabilization is not included. Example creates a convection cell between 2 opposing walls, and has a parabolic velocity BC on the top to make it more interesting.

Added d_rho_dT(...) inline function to low_mach_navier_stokes_base.h for computing the derivative of density, rho, with respect to temperature, T.