[Boone]

Hi everyone,

I would like to investigate the numerical scheme effects for the discretization of Navier-Stokes equations with relative coarse grids.

I often heard that the upwind schemes are more dissipative than centered schemes. Could you explain me why ?

Is a 4th order centered scheme less dissipative than a 2nd order centered scheme ?

Thanks a lot for your answers !
Boone

[FMDenaro]

Originally Posted by Boone

Hi everyone,

I would like to investigate the numerical scheme effects for the discretization of Navier-Stokes equations with relative coarse grids.

I often heard that the upwind schemes are more dissipative than centered schemes. Could you explain me why ?

Is a 4th order centered scheme less dissipative than a 2nd order centered scheme ?

Thanks a lot for your answers !
Boone

What you are asking is one of the basic paragraph in any CFD textbook.
Have a look here
https://www.researchgate.net/profile...+dynamics+.pdf

[sbaffini]

I'll play the devil against the Filippo effort to guide you into searching yourself the answer and just give it here for you to consume it. I assume we are talking about convection here:

- Upwind schemes are dissipative while, for uniform grids, centered schemes are not (like not at all). The reason is in the truncation error of the two schemes and the symmetry breaking of the upwind one. In practice, the truncation error of the upwind scheme doesn't cancel certain derivatives, which reappear as numerical diffusion in the equation you are actually solving. Symmetry of the central scheme is such that the same terms instead disappear and so does numerical diffusion, but dispersion exists for both (yet the diffusion of upwind kills that).

- For uniform grids 4th and 2nd order central schemes have both the same, null, numerical diffusion. The 4th order scheme has less dispersion error than the 2nd order one.

Just for completeness, the dispersion error is the one causing different wavelengths of the solution to travel at different, numerically induced, speeds.

[Boone]

Thank you very much ! I more clear now !