# grid independence and first order upwind scheme

 Register Blogs Members List Search Today's Posts Mark Forums Read

 February 20, 2014, 04:41 grid independence and first order upwind scheme #1 Member   yehanyu Join Date: Mar 2012 Location: Beijing, China Posts: 41 Rep Power: 6 Hi, everybody. Recently I read the AIAA "Editorial Policy Statement on Numerical and Experimental Accuracy". (http://arc.aiaa.org/page/numericalan...mentalaccuracy) This guide requires that numerical algorithm solving partial differential equations should be at least formally second-order accurate in space. I know that this is because first order schemes will introduce too much numerical dissipation. However, numerical dissipation can be reduced by refining the grid. Therefore, I have a question. If I use first order scheme and obtained a grid-independent solution by successively refining the grid, then is the solution acceptable? (For my problem, high order schemes often make the solution process unstable, and even diverge. ) Thank you very much.

 February 20, 2014, 07:16 #2 Senior Member   duri Join Date: May 2010 Posts: 160 Rep Power: 8 This policy related question, AIAA editors are best people to answer this question. But from practical point of view, no one uses first order results for their application. Also, there is no point is working on first order with bulky mesh. It will increase unnecessary computational resource and time. If you are concerned about stability of high order scheme, then please post what are you trying to do. FMDenaro likes this.

 February 20, 2014, 07:46 #3 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 2,606 Rep Power: 33 using first order upwind for generally used high Re number flows, 1) is not really suitable to reach a grid independent solution in terms of DNS 2) is not usable for LES as it imply a dramatic smoothing of the resolved frequency 3) can be some how acceptable in RANS as long as the turbulence modelling overcome the first order magnitude of the local truncation error. In conclusion, very low Re laminar flows can be resolved but are often academic test-cases. High-order schemes are accurate and stable (conditionally), if you have a numerical instability something does not work correctly.

February 20, 2014, 23:33
#4
Member

yehanyu
Join Date: Mar 2012
Location: Beijing, China
Posts: 41
Rep Power: 6
Quote:
 Originally Posted by FMDenaro using first order upwind for generally used high Re number flows, 1) is not really suitable to reach a grid independent solution in terms of DNS 2) is not usable for LES as it imply a dramatic smoothing of the resolved frequency 3) can be some how acceptable in RANS as long as the turbulence modelling overcome the first order magnitude of the local truncation error. In conclusion, very low Re laminar flows can be resolved but are often academic test-cases. High-order schemes are accurate and stable (conditionally), if you have a numerical instability something does not work correctly.
You said that first order upwind scheme is "some how acceptable" in RANS. Which of the following do you refer to?
(1) Use first-order upwind scheme for both the momentum equations and the turbulence transport equations;
(2) Use high-order schemes for the momentum equations, while use first-order upwind scheme for the turbulence transport equations.

February 24, 2014, 00:09
#5
Senior Member

Julien de Charentenay
Join Date: Jun 2009
Location: Australia
Posts: 230
Rep Power: 10
Quote:
 Originally Posted by duri But from practical point of view, no one uses first order results for their application.
While I do not discuss the point that Duri is trying to make, the above sentence would gaiin from being more accurately defined.

no one: the statement is obviously an expression of speech and overgeneralisation;

uses first order results for their application: if you are using a commercial software, you are likely to be using a spatial discretisation scheme that is not strictly second-order. It is more likely to be a second-order scheme with (a) a limiter, and (b) a blending with a first order. Furthermore, the second-order is achieved by an explicit correction. The implicit part is very likely to be first order only.

I would personally reformulate the statement as follows: Best practice would recommend the use of second-order spatial discretisation scheme.
__________________
---
Julien de Charentenay

 Tags first order, grid dependence, numerical dissipation, second order

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is OffTrackbacks are On Pingbacks are On Refbacks are On Forum Rules

All times are GMT -4. The time now is 12:39.