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 Mehdi June 20, 2003 15:00

Oscillation of a upwind scheme

I am coding an upwind scheme with adaptative mesh to solve an MHD problem with a strong shock. I am using a 2 stage Runge-Kutta scheme for stepping in time.

I have problem to converge, since my solution start to oscillate very quickly (5 or 6 iterations), the osciallation become verry strong and crash the solution.

These oscillation seems to come from the shock and expand to all the space domain. The oscialltion frequency is the same of the grid, so refining more does'nt change resolve the problem.

- I want to know what kind of solution I have to damp such oscialltion and make my solution converge. - Should I add a terme in d2_U/d_x to add an actificial viscosity in my solver ? What consequence it will have on the final solution.

Thank you

 Ravi June 20, 2003 16:29

Re: Oscillation of a upwind scheme

I assume you are using higher order upwinding. Upwind schemes are subject to oscillations near shocks. You can use some limiter ( e.g. minmod, vanleer..) to restrit the scheme to first order near shocks to make the scheme more dissipative and avoid oscillations.

Typically, they add artificial viscosity for central difference schemes as it has no dissipation..( so the term artificial or numerical viscosity)

I hope this helps.

Ravi

 Mehdi June 23, 2003 12:55

Re: Oscillation of a upwind scheme

Thank you for you answer Ravi

In fact, I am using a second order in space and time upwind MUSCL scheme. during the reconstruction I use a minmod type diffusive limiter to reconstruct the cell's edges variables (Barth limiter). Despite I am forcing this limiter to 0 ( forcing the scheme to be just a first order in space all the time), I still have the same oscillations that are coming form the shock.

Turning on or off the grid refinement doesn't change anything too as I said.

How can I remove such oscillation that make my solution diverge ?

PS : I am simulating a supersonci plasma shock (M=10)

 versi June 24, 2003 20:51

Re: Oscillation of a upwind scheme

Did you experience the so called carbuncle artifact for blunt body in supersonics? there are much work done on it. You can see recent (2002-2003) JCP paper. It seems that all 1D-based Riemann -type scheme will face such "carbuncle artifact" in hypersonics.