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 Girish Bhandari January 9, 2001 20:04

Artificial Viscosity

Hello,

Can anyone suggest an artificial viscosity reference other than Anderson's book or pressure based artificial viscosity? Thanks in advance.

GB

 John C. Chien January 9, 2001 21:49

Re: Artificial Viscosity

(1). There are two occasions when the word artificial viscosity is used. (2). In density based, transient compressible flow formulation, an explicit artificial viscosity term is added to the governing original equation for stability reason. It has nothing to do with real viscosity at all. But the term added is always of higher order form. It should be called stability improvement term or damping function term. (3). In the pressure-based formulation (or incompressible flow), the lower-order method , such as the upwind method, can be expanded to show the numerical diffusion term or effect. The second-order numerical diffusion term is sometimes called the artificial viscosity term, which exists implicitly through the first order formulation. It should be called implicit numerical diffusion effect, since no additional term is added to the original equation.

 Girish Bhandari January 11, 2001 10:38

Re: Artificial Viscosity

John, I agree on your points. Could you pl suggest a few good references on Artificial Viscosity(damping)? Thanks.--GB

 John C. Chien January 11, 2001 15:40

Re: Artificial Viscosity

(1). I think, the book by Anderson, Tannehill and Pletcher, " Computational Fluid Mechanics and Heat Transfer" is the place to start. (2). The book covers both the explicit and implicit "artificial viscosity" in many places. (3). In most cases, the explicit "artificial viscosity" terms are invented by the author of his method, therefore, you will have to dig out his original paper to see the detailed function. This is another "black art" of CFD. If you don't like his form of "artificial viscosity", you are free to invent your own. (4). It would be fun to watch the passenger of a rocket ship, when you told him that the rocket ship was designed based on your CFD analysis using your secret formula of "artificial viscosity" to stabilize the solution.

 Girish Bhandari January 11, 2001 16:28

Re: Artificial Viscosity

You are right John. Its all right as long as it gives you C olor F ul D ollars.

 John C. Chien January 13, 2001 14:22

Re: Artificial Viscosity

(1). It is interesting to know that "artificial viscosity" did not come from the market side, but rather came from academic research side. (2). In a way, CFD is polluted right from the begining. For those who have to publish papers to survive, they thought they had invented something quite useful. (3). You can say that, most density based formulations containing artificial viscosity, also produce artificial solutions. And at one time, a journal was forced to reject the papers based on first-order method (upwind method), because they thought that the true solution could be found somewhere in the higher-order method domain. (4). Since the free market is free to eat anything , the artificial viscosity will be around for a long time, as long as it is packaged or recycled properly. I mean, you are not going to see " CFD with artificial viscosity" on the label of the package. Most likely, it will be "CFD using well-known method developed by Prof.xyz, from first-class university-abc". (5). Your question is very important, because modern CFD development were largely based on these artificial viscosity effect, first-order mwthod, or limiters. There will be long term and short term effect, so make sure that you know what you are eating. (In some places, dog meat was sold with lamb on the label, as news said in very old country. The lamb label was for the officials, because customers liked the dog meat. It is quite possible that dog meat was the only thing available in the stone age (like CFD with artificial viscosity), and later it got integrated into people's DNA. After that, it became the story in the news in the old country.)

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