OpenFOAM Schemes

In this short post, the effect of numerical scheme on convection term is investigated. The following problem is considered. More information about this problem can be found in Introduction to Computational Fluid Dynamics [1].

flow domain for false diffusion
flow domain for false diffusion

In the absence of physical diffusion, we expect to have a sharp interface along the square diameter, so the value below diameter is 0 and the value over the diameter is 100

now, we are looking at the numerical results:

  • upwind
upwind scheme on divergence term
upwind scheme on divergence term

upwind is first order bounded scheme, thus the value would be between [0,100] but it adds numerical diffusion, so the interface does  not remain sharp anymore.

  • linear
linear scheme on divergence term

linear is unbounded second order scheme, so the interface is sharp but the value near interface become unbounded, which may lead to numerical instability.

  • limitedLinear
limitedLinear scheme on divergence term
limitedLinear scheme on divergence term

It is a hybrid scheme, so it both preserve the interface and boundenness.

download code and test case

 

reference


  1. Versteeg, H.K. and Malalasekera, W., 2007. An introduction to computational fluid dynamics: the finite volume method. Pearson Education.

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