# Solving Compressible Euler in Primitive Variables with Galerkin P1 FEM

I have implemented a small compressible Euler solver, discretizing in primitive variables (rho, u, v, p) with standard Galerkin FEM P1 triangular elements, and mixed isotropic and anisotropic/streamline diffusion for stabilization.

I have verified the solver on several test cases with shock tube, double shocks, and flow over bumps, so it seems to work fine except for some oscillations (as the artificial diffusion isn't shock capturing or monoticity preserving).

Now I'm trying to validate a simple 2D static oblique shock test case for a unit square which should be simple and has an analytical solution. With top/left boundary conditions Ma_in = 2, rho_in = 1, u_in = cos(10 deg), v_in = sin(10 deg), p_in = 0.1786, bottom slip (v = 0), the analytic solution should be a shock at 29.3 degrees and Ma = 1.64 at the outlet (right boundary). My solver converges just fine and resolves the shock, however the solution is inverted after the shock, Ma 2.4, density 0.65 instead of 1.46 etc.

I cannot seem to find the error, especially as the dual shock problem solves fine. Could this be to using non-conservative/primitive variables? Any ideas at all would be helpful.

• Very interesting. I dont know the answer. Could you try to set the exact solution as initial condition and see where your solver converges to ? – cfdlab Oct 29 '18 at 10:10
• You can also check if the solution you got satisfies jump conditions and entropy condition. – cfdlab Oct 29 '18 at 10:13
• It's hard to see how we can be of much help here on this forum: We don't know the code, and we can't inspect the output. There's a bug somewhere in your code in all likelihood, but there's little anyone can do who doesn't have access to it. – Wolfgang Bangerth Oct 30 '18 at 3:09