Am using a first-order upwind method for solving a hyperbolic system. Am getting lots of oscillations with fine mesh, things with coarse mesh are fine, i.e. the solution changes and the oscillations appear after increasing the number of cells with space.

Is it possible for upwind methods to be very much oscillatory?

What is the best first-order upwind method to use?

Hi Lee,

I sugest you using the ADBQUICKEST scheme. See International Journal for Numerical Methods in Fluids, Article in Press by Ferreira, V.G. et. al. 2008.

Good Luck Ferreira

what is the difference between the quick scheme

I should write my question in a different way, in hope of a reply!

I have one wave only a stationary discontinuity. I known that stationary discontinuities have the largest dissipation leading to spreading of the wave as time increases, please correct me if am wrong.

No problems with time for me. If I increase the number of cells, fine mesh, I find that a huge dissipation leading to damage of the wave(s)- at the beginning and at the end of the contact wave.

Is this possible with upwind first order schemes. Does it mean that the system losses his hyperbolicity ?

... it is bounded ...

when you solve a system it retain its mathematical characters, if it is a hyperbolic then it remains so. what is the method you are using? are you using a FV or FE method if FV which method? I used a upwind in a artificial compressibility and it came out to be oscillation in pressure field and that is because you should use central for any term that is related to pressure.

The system is hyperbolic for incompressible liquid-liquid two-phase flow. Have used a very simple upwind FV. As I said I have a stationary discontinuity i.e. one contact wave corresponding to one eigenvalue which is a linearly degenerate, and two injected discontinuities these are just point source terms. So sharp discontinuities will appear. The numerical solutions are mesh (grid) dependent. Problems starts with fine mesh. Is it because of the linearly degenerate? Or the mathematical model or the point source terms effect the hyperbolicity of the model?