Hi.

I'm working on my own incompressible CFD-code (finite elements) ans was wondering if I should use upwinding. Re < 100 000. If you have any good references about the subject, I'd appreciate if you would could share the information. Journals I've found so far deal with shocks etc.

Thanks.

Jarmo

i have read papers where upwind schemes are used to solve incompressible flows but the principle behind upwind schemes only makes sense when there is large variation in the characteristic direction which doesn't happen in incompressible flow. ie i think it is a waste of time for incompressible flows. it is is better to use pressure based schemes (SIMPLE etc) or preconditioned time iterative scheme both with simple central differencing

(1). AMD-VOL-34, 1979, "Finite Element Methods for Convection Dominated Flows", edited by T.J.R. Hughes, published by The American Society of Mechanical Engineers.(2). There are many papers dealing with "upwind method" by leading experts in FEM. (3). It is not my field of research, I can't comment on your FEM. But the need to use upwind method for the convection term occur when the local cell Reynolds number is greater than 2.0. Most CFD books should cover this issue and it is fairly straight forward in FDM.

Hi,

I do not know about finite element approach, but, in a sense, structural mesh is just a specific case, and there upstream differencing is quite useful. It seems, to improve the condition number of the matrix, one have to use some kind of upstream differencing anyway. I use it for incompressible flow, structured mesh, natural variables, and without it high-Re calculations are almost impossible. However, strightforward application leads to poor accuracy. So, Leonard method is widely used, and here is the reference.

Leonard B.P. A stable and accurate convective modeling procedure based on quadratic upstream interpolation. Comp. Meth. Appl. Mech. c Eng., 1979, v.19, No.1, 59-98.

Hope this may help. Sergei

Thank for the references, John and Sergei. I will take a look at those.

I would definitely use this method with Finite Differences, also in high-Re problems... Right now it looks like I don't need to worry about it but improve my code some other way.

Jarmo

Hi Jarmo,

to upwind or not to upwind that is that question!

The topic of treatment of the advection terms is arguably the greatest cause of debate, research, controversy, etc, of the past 25 years in CFD. Obviously a brief response on an on-line discussion is going to be inadequate to fully understand the implications! But, some suggestions to get you started:

1. Start with the text material: Ferziger and Peric cover FD.FV, and FEM with emphasis on FV and an excellent discussion of numerical errors!

2. Hirsch devotes numerous chapers of his 2 volume text to the topic...it is, however much less accessable to the beginnner that F & P above!

3. Cover the references, starting with the review articles from the texts above then moving on to the more frequently cited papers, less frequently cited, etc.

It has been my experience that a structured search starting out broad and narrowing in is much more effective than randomly reading papers.....and the volume of papers on this particular topic necessitates such an approach!

Best of luck......................................Duane

Whi do you not use the SMART? I like it very much.

Good luck.