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 Giovanni Ieria November 24, 1999 11:21

First Order Upwind

I am a student of Calabria University (Italy), I am developing a thesis about CFD for ship. I have not undestood Firs Order Upwind (reading FLUENT manual 17-11) very well. May you help me? Thanking in advance, I remain.

 Michael Soso November 24, 1999 17:28

Re: First Order Upwind

The first thing that you need to grasp is the concept of how diffusion works in fluids. Upon discretisation of the governing equations in CFD, the same sort of process occurs because of numerical roundoff, etc. When using a first order upwind scheme to discretise the the solution, numerical diffusion can easily occur(bad thing). When using a second order upwind scheme the instance of numerical diffusion is greatly reduced. Basically, converge your solution with the first order scheme, then switch to the second order scheme and converge again.

 John C. Chien November 25, 1999 01:47

Re: First Order Upwind

(1). Looks like that the FLUENT manual is hard to understand. My suggestion is: go through that section a couple of more times, and if you still don't understand it, ask your friend to read it for you. (2). I had used the code for a couple of years, but I didn't try to read the manual at all. So, even if you think you had the answer, it may not be the one used in the code. (3). You don't care about the inside of the code (you can't see the inside of it anyway), the important thing is: whether you will be able to use the code to solve your problem. If the solution is good, it's fine. Otherwise, if you can't get the solution, too bad. And if you can't get the solution by selecting the upwind difference method, you are out of luck. (4). Methods related to the upwind difference can be found in most CFD books.

 Duane Baker November 30, 1999 19:43

Re: First Order Upwind

Hi Giovanni,

first order upwind treatment of the advection terms is covered very thouroughly by Ferziger and Peric's book "Numerical Computation of Fluid Dynamics" 2nd ed. I believe the main conclusions are on about p 83 and a fairly accurate quote is:

First order upwind (UDS) is inaccurate and should not be used. It results in significant false diffusion both in the streamwise and cross-stream directions and will not give accrate results on reasonable grids, especially in 3D.

The scheme originated in the early 70's when a big problem was 20 X 20 grid and the only way to get a solution to converge with iterative methods was to use UDS (because of the cell Peclet No limitation for CDS and other schemes and the negative effect on covergence due to the loss of diagonal dominance for high cell Pe with any scheme other than UDS on such coarse grids). The UDS scheme will always give a smooth solution which fools the uneduacted user or client into thinking that it is a good solution. A very serious problem occurs with this scheme when the prediction of sharp gradients is paramount (such as in in near wall momentum and heat transfer) the UDS will always be too diffusive and sometimes the gradient is off by 100% or more even when the overall solution looks pretty good!

My advice, just stay away from UDS except for an initial guess which will converge fast or in the deffered correction technique...again read F&P!

Regards,

Duane Baker

Read F&P and do the examples!

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