Solving the 2D Euler over a circular bump FDMethod
 

I developed a code to solve the steady state Euler equations in a 2D channel with a straight upper wall and a 10% circular bump on the bottom wall. I am using a MacCormack scheme (predictor/corrector) to solve the Euler equations on a body fitted mesh. When I run the code, I experience problems at the inlet. The Mach# on the nodes following the inlet will start decreasing throughout the iterations and I think this is why the solution is divering. I am using non reflecting boundary conditions. The inlet conditions are Mach#=0.5, density=1, Pressur=1/gamma. I could not find what the problem and am desperate for solutions. Thanks

Re: Solving the 2D Euler over a circular bump FDMe
 

U have to be very careful at the inlet specially in your case when the mach no is less that one.You have to find all the characteristics for the governing equation and decide which characteristics should be set by u and which should be set by the code.Ask if you need more help on this

Re: Solving the 2D Euler over a circular bump FDMe
 

Thanks for the advice. I was able to solve the problem at the inlet. Now my problem is convergence. I can see oscillations on the mach profile for the bottom boundary. The oscillations start at two places: a bit downstream of the leading edge and a bit downstraem of the trailing edge. Basically where there is a sharp transition from low mach number to high mach number. My question is could this method be unstable for my problem, (even though I was told it is not) and what can be done to get stability. I tried refining the mesh which didn't work, and playing with the CFL number only delayed the divergence. I included a dissipation factor based on velocity only, that is added to my flux matrices F and G. This again did not work. I am stuck at this point and need some suggestions. Thanks in advance.

Re: Solving the 2D Euler over a circular bump FDMe
 

u seem to have non -physical waves running around which I think is related to boundary conditions .I will tell u if come accross something

Can some body tell me what are the correct boundary conditions for this problem? I assume a satic pressure at outlet o that with isentropic relations I have the inlet total p. then we need 3 more in 2D .among them one is extrapolation which I use riemann invariant extrapolation,but what are the others when we have the inlet mach number?