Thanks Praveen!!

Ruben OP:

I'm writting a code for solving the Euler equations of compressible flow.

I'm interested in state state solutions and I have problems with the oscillations. Even in the subsonic case I have spurious oscillations and the convergence is too slow. I think that I need a time integration scheme with damping. What scheme can I use?

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diaw comments:

After all has been said & argued on this thread, & after spending a while reviewing both Euler & Potential derivations & equations forms, I must say that I fail to see a useful valid connection between the two.

Potential flow:

Irrotational flow => transform via u=d(phi)/dx ; v=d(phi)/dy

=> d2(phi)/dx2 + d2(phi)/dy2 =0

Euler flow (weak form):

d()/dt + u.d()/dx + v.d()/dy = f(x,y,t)

The two are completely different animals:

1. The Laplace equation is going to either decay/grow in time, if a d(phi)/dt is bolted on & dependent on the sign used & possibly some forcing function. If in steady form, then we have a nice smooth shape.

2. Euler eqn is a convection flow which is inherently unstable & wants to produce instability, waves & the like. Not too smooth at all...

If you really begin to look deeply into the physics of what these forms actually represent, they are very different.

I have no doubt that the OP sees waves - & so he should with a good algorithm. It is a poor algorithm that adds unwanted numeric viscosity.

diaw...

Thnaks for your comments diaw.

[moein_joon27]

what are the correct boundary conditions for this problem? we need 4 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?