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 Zhou Yongcheng January 7, 2001 22:40

Dear all:

Could anyone tell me how to deal with nolinear terms in N-S equations with ADI method and the pressure terms?

Zhou Yongcheng

 John C. Chien January 8, 2001 20:02

(1). The book by Anderson, Tannehill and Pletcher, "Computational Fluid Mechanics and Heat Transfer" has a chapter on numerical method of Navier-Stokes, which includes ADI related schemes. (2). You can read the text and find the reference materials.

Suggest add to it the other book 'Applied Numerical Methods in Engineering' by Carnahan, Wilkes and Luther.

 A. Rajani Kumar January 9, 2001 05:29

First I want to say that , if you are using ADI for 2D N-S equations then it is ok. For 3D N-S equations you better go for LU Approximations(example: LU-SGS by A.Jameson).

1)We will treat Non-linear viscous terms explicitly. 2)pressure term will be expressed in terms of u,v,w,rho and e.

 Dean Schrage January 17, 2001 12:04

Re: ADI of N-S equations (Paper ref.e w. Abstract)

Hi,Yongcheng

I published a conference paper on this topic last year. A starting link can be found at:

http://edwww.lerc.nasa.gov/thermal/t...urses.html#PAP

I grabed the abstract from the file for your review. See below. The non-linear terms are linearized by belating 1 time step, the leading velocity term. The advection terms are split in a fashion analogous to the diffusion terms by following the Brian adaption. To my knowledge this had not been done before. The pressure term is simply a source to the AD equation. The ADI-Brian routine applies 3-sweeps and is 3D. The third dimension is no problem. I think the performance was excellent. It outpaces SOR by x30 and this was for a 2D problem in which I was executing the 3rd sweep unnecessarily.

Hope this helps.

regards

Dean

 Dean Schrage January 18, 2001 08:58

Upon reviewing my archives, I've found this image:

http://www.ctacourse.homepage.com/Ga...FrontQuick.jpg

This was derived with the ADI-Brian simulation and is a simulation of the AD equation with infinite Peclet number. Flat front simulation. The solution is derived using the modulator function as discussed in my abstract. It clearly shows the mitigation of both diffusion and dispersion errors.

I can't say enough about ADI. It is an excellent adaptable method, having even used it in phase change heat transfer simulations.

regards

Dean

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