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 .
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 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 is unbounded second order scheme, so the interface is sharp but the value near interface become unbounded, which may lead to numerical instability.
It is a hybrid scheme, so it both preserve the interface and boundenness.
- Versteeg, H.K. and Malalasekera, W., 2007. An introduction to computational fluid dynamics: the finite volume method. Pearson Education.