[bigorneault]

I am looking for a convection scheme with the following requierement

- structured grids
- implicit finite volume (must allow large time step)
- ideally 3rd order accurate
- monotonic, positivity preserving
- low speed, compressible flow

I have implemented QUICK and whilst the deferred correction schemes improve the numerical stability of the linear systems, one of the fundamental problems of this scheme remains, with the solution field often exhibiting spurious, non-physical, oscillations.

I am aware that Leonard has applied a number of flux–limiter schemes to the basic third order upwind biased method. Leonard efforts (both numerically and acronymically) lead to SHARP, ULTRA-SHARP, ULTIMATE, ULTIMATE QUICKEST, UTOPIA, NIRVANA, ENIGMATIC, MACHO, COSMIC and many other schemes. Other authors also contributed with their schemes and acronyms like UMIST and CHARM ...

I must admit I am a bit confused about which scheme I should consider for my problem.
Suggestion are welcome.

[michujo]

Hi, check out the book by Versteeg&Malalasekera 2nd Edition. In this revised and extended edition there's a whole section dedicated to TVD schemes where you'll find a bunch of flux limiter functions (Van Leer, SUPERBEE, Min-Mod, ...) as well as practical information as to how to implement them in your CFD code.

I hope it helps.

Cheers,
Michujo.

[bigorneault]

Originally Posted by michujo

Hi, check out the book by Versteeg&Malalasekera 2nd Edition. In this revised and extended edition there's a whole section dedicated to TVD schemes where you'll find a bunch of flux limiter functions (Van Leer, SUPERBEE, Min-Mod, ...) as well as practical information as to how to implement them in your CFD code.

I hope it helps.

Cheers,
Michujo.

Thanks you for the suggestion. I have already read this (very good) book and I considered implementing a TVD method. My concern is that these methods seem to be only second order at best and would prefer a third order scheme.

[FMDenaro]

Originally Posted by bigorneault

Thanks you for the suggestion. I have already read this (very good) book and I considered implementing a TVD method. My concern is that these methods seem to be only second order at best and would prefer a third order scheme.

formally, any limiter applied on high order scheme degrades the accuracy near discontinuity... you must accept that ...
I suggest also trying ENO/WENO schemes...

[bigorneault]

Originally Posted by FMDenaro

formally, any limiter applied on high order scheme degrades the accuracy near discontinuity... you must accept that ...
I suggest also trying ENO/WENO schemes...

Thank. I have looked quickly to the ENO/WENO methods. To be honest, but I did not understand much and this is why I tried to use simpler FV methods. Do you know a good and easy tutorial/book on the subject?

EDIT : I also have a requierement to try to minimize the lenght of the stencil, which is not easy with ENO from what I understand. The TVD scheme with fixed stencil size is then probably the best solution for the moment.