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Old   October 10, 2002, 08:22
Default Conservative finite difference scheme?
Linfeng BI
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Hi all, I am developing a LES code firstly to compute a back-facing step problem using finite difference method. But I simply cannot keep the flux the same value at cross sections before and after the step. Though not very large, there always exists this difference. I guess it is the FD scheme that causes this problem. And some other reasons?

So what i want to know is how to build up a conservative FD scheme for NS equations(as well as filtered NS eqns)--for mass, momentum and energy. Is there any general remarks or constrains when building such schems?

Thanks, Linfeng
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Old   October 10, 2002, 13:17
Default Re: Conservative finite difference scheme?
frederic felten
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Hi there,

check out the following papers:

[1]- Morinishi, Lund, Vasilyev and Moin, "Fully conservative Higher Order Finite Difference Schemes for Incompressible flow", Journal of Computational Physics, Vol 143, pp 90-124, 1998.

[2]- Vasilyev, "Higher Order finite difference schemes on non-uniform meshes with good conservation properties", Journal of Computational Physics, Vol 157, pp 870-891, 2000.

[3]- Felten and Lund "Critical comparison of the collocated and staggered grid arrangements for incompressible turbulent flows", Proceedings of the 3rd AFOSR International Conference on DNS/LES, Arlington, Tx, Aug. 5th-9th 2001.

You can actually download [1] and [3] from my website:, and for [2] go to

Reference [3] is currently being reworked and will be submitted soon to the JCP. A link on my website will create such that a preprint can be downloaded!!

I hope this helps, sincerely,

Frederic Felten.
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