DRP schemes
 

Dispersion relation scheme is aimed to resolve a problem with less number of grids by minimizing dispersion and dissipation. Most well known classical papers on DRP are [1] [2]


Here temporal and space discretization is optimized separately. Later combined temporal and spatial discretization is explored in
http://www.sciencedirect.com/science...21999110000331

http://www.sciencedirect.com/science...2199910500416X

I could see a lot of papers now using those approaches. They are quantifying everything for advection equation. My test shows that later one shows some improvement in advection equation but I'm not happy in Euler equation. Please give me your personal experience or opinion on these analyses.

Never used but I am not surprised of some problems in the Euler equations. What happened to your simulations?

Sir,
Some of the benchmark problems I have tried, they performed poor than classical methods :eek: in terms of dissipation, dispersion and stability limit in terms of CFL number.

Even on smooth solutions?

I tried only on Advection equation with Gaussian initial condition where time and space DRP worked well. For some 1-D and 2-D Euler equation classical and some other RK performed better than DRP. So far I didn't try smooth solution. DRP is commonly used by some Aero-acoustic peoples and turbulence peoples. Former one mostly deals with the flow having shocks so it should be good for problems with shocks. Space-Time DRP is complicated and in high speed flows it's very difficult to say discretization style used, because in FVM residual calculation looks like central and second order but it will be first order because of Reimann solver in the solver so I can't simply come to one solid conclusion.

Why don't you show some of your results so that we can talk of a more specific issue?

I shall share once I complete the report. I saw one paper slightly against DRP

https://www.researchgate.net/profile...cillations.pdf

Ok, unfortunately the modified wavenumber analysis is done one the derivative of a function not of the product as happens in the non linear term.
The Burgers model equation would be much more appropriate to test the spectral resolution.

We could do that but Fourier analysis is linear so multiplication of the same family of the variable not defined.

Well, it is possible to extend the modified wavenumber analysis to the convective non-linear term. Just using the product of the two linear Fourier expression