Artificial viscosity
Hello Everyone
I'm interested in the problems of nature convection of cold water in an enclosures with high Rayleigh number. And it is very important problem for me to compare the artificial viscosity of Patancar's Power Law Scheme and Leonard's QUICK Sheme. (I use the SIMPLE and SIMPLER) But I have no idea how could I do it. Does anyone know? Would you pleased to write me? Thank you very much. Eugene 
Re: Artificial viscosity
(1). The artificial viscosity is really "artificial". (2). This happened when people started using methods other than the centraldifference scheme for the convection terms for stability reasons. These methods bring in life because they are more stable than the centraldifference scheme. The bad news is they also change the behavior of the solution. (3). To make the comparison, one first tried to write the new methods (say upwind method, etc...) to emulate the centraldifference scheme, "plus additional terms". (4). So, if one then substract the centraldifference scheme equation from the equation of the new method, obviously, he is going to have the "extra additional terms". (5). These extra terms can be viewed as the deviation from the basic centraldifference scheme behavior. In the upwind difference case, the extra term remained after substracting the equation with centraldifference scheme, is of the secondorder form. And the original diffusion term is also of the secondorder, (these are diffusion terms with the viscosity in front of them) (6). Thus the extra term in the upwind difference scheme equation behave like a secondorder diffusion term. So, the coefficient is called "artificial viscosity" when compared with the similar secondorder term,which have the molecular viscosity in front of them. (7). Physically, they have nothing to do with the real viscosity. The order of magnitude of the coefficient (the artificial viscosity) is much larger than the molecular viscosity. As a result, the effect on the calculated solution becomes quite "visible". Sometimes, it will give you wrong behavior in solution. But this term can be minimized by decreasing the cell size or grid spacing. (8). In the early days, sometimes artificial viscosity terms or diffusion terms are created and added to the viscous or inviscid equations to stabilize the solution. But that is a different story.

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