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I. Dotsikas April 17, 1999 14:11

Diffusion / convection
Hi, it's clear that the use of Upwind-Diskretisation introduces a quite big error in a calculation. (nummerical diffussion). There are some Methode to diminish this Diffusion, the use of an second Order Approximation is one reasonable Method. An other Method is to use the Power Law or Hybrid Method (see Patankar) or a differed Corection schema or Quick. The most CFD Books stop at this point and don't write furtur abou the diffusion / convection Problem. * Is there a publication comparing all these Methods with each other?

* where can I found some Information about Higher Order modells for Diffusion / convection coupling ?

I am interested on books and artickles introducing and explaining such methods.

John C. Chien April 20, 1999 13:15

Re: Diffusion / convection
(1). I am not sure that the use of the up-wind difference will introduce big error in a calculation. (2). Higher order scheme is not equavalent to higher accuracy solution. (3). It simply says that lower order scheme requires more mesh points to capture the truncated higher order terms. (4). The size of the truncated higher order terms depend on the problem to be solved ( solution dependent), the mesh orientation ( coordinate system), the mesh size distribution. These can be optimized in such a way that the size of the truncated higher order term is minimized. (5). The way to do is to study the solution of a particular problem at hand in great detail first. Then with the proper selection of the coordinate system ( mesh orientation ), and the mesh density distribution, one can minimize the truncation error. The body aligned mesh, the adaptive mesh are two methods to achieve this goal. (6). Even if you still insist on using the fixed Cartesian coordinates, simply adding more mesh points will solve the problem. With workstations having 128Meg RAM everywhere, it is hard to get poor results from up-wind methods. But if you still think that solution can only be obtained by using a 41x41 mesh for high Reynolds number problem in Cartesian coordinates, then you will be facing that big error all the time. (7). There is another problem called " consistency ", that is the finite difference equation must approach its original differential form as the mesh size approaches zero. Here we are assuming that the consistency is satisfied. (8). So, Don't Try the Coarse Mesh Solution!!!

anay luketa-hanlin April 21, 1999 16:39

Re: Diffusion / convection
Yes, There have been many improvements on the QUICK method. There is a good journal article on one in the JOURNAL OF COMPUTATIONAL PHYSICS 98, 108-118 (1992) by T. Hayase, et. al. I am using it right now and so far it has performed very well. I have found it to have very low numerical diffusion. This paper compares CD and UPWIND schemes and other QUICK schemes. Very good paper.


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