CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > Main CFD Forum

What's the future use for high-order END scheme

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

Reply
 
LinkBack Thread Tools Display Modes
Old   December 5, 2001, 05:17
Default What's the future use for high-order END scheme
  #1
Yang
Guest
 
Posts: n/a
Hi, everyone

Now, I'm working on high-order ENO schemes for complex flow simulations. I'd like to get more wide commentary for the future use of high-order ENO schemes mainly based on Harton's method, as well as compareson with high-order compact schemes.

Thanks in advance Yang
  Reply With Quote

Old   December 5, 2001, 23:43
Default Re: What's the future use for high-order END schem
  #2
Paul
Guest
 
Posts: n/a
ENO and WENO are originally designed for shock-capturing. The basic idea behind these two methods is that an upwind scheme will be dominant near the discontinuity, which definitely will lead to a distinct numerical dissipation part in the scheme. For general application in laminar flow, ENO or WENO is not a good choice because you have to spend much time in selecing the grid stencil. In these cases, high-order compact scheme may perform better. For turbulent flow, there is no general idea if this dissipation in ENO or WENO will damp the turbulent fluctuations. Nevertheless, compact scheme has been successfully used in turbulence simulation. With the increasing of the formal order of ENO and WENO( they can be 9-11th order, see a JCP paper in 2000), the numerical dissipation inside the scheme tend to be smaller, the main problem in using ENO and WENO thus is their CPU intensivity. In my conclusion 1) For high-resolution shock-capturing, ENO or WENO is

highly recommanded. 2) For laminar flow, other high-order method is

preferred unless you don't care the computation

time and want to use the dissipation in the ENO/WENO

to stabilize your computation. 3) For turbulent flow, you had better use other

schemes.

  Reply With Quote

Old   December 6, 2001, 03:42
Default Re: What's the future use for high-order END schem
  #3
Yang
Guest
 
Posts: n/a
Hi, Paul Thanks for your response. I basically agree with your argument. As you know, ENO scheme is based on piecewise polynomial reconstruction, and this reconstruction can be extended to 2D and 3D problem with the full base of polynomial terms, that to say, including all high-order cross terms. But, high-order compact schemes are derived from one direction stencil, so, for 2D or 3D cases, high-order cross terms were neglected. I'm wondering which kind of effects these cross terms will take for the simulation of turbulent flow or some other complex flow. If these cross terms are neglected from ENO scheme, the CPU time will drop quite a lot. By the way, my another question is: what's the relation between high-order discretization scheme and high-order grid transformation?
  Reply With Quote

Old   December 7, 2001, 01:09
Default Re: What's the future use for high-order END schem
  #4
Paul
Guest
 
Posts: n/a
Hello, Yang. ENO/WENO do use the method your described in high-dimension-extension. And they also use conventional method (one direction stencil) in such extension. As I know, these two methods are equivalent as long as the derivatives in the PDEs are well approximated.

For your second eqestion. In book `Numerical grid generation, foundations and applications' by Thompson et al., there is an argument about the the influence of the truncation errors of the grid generation on the numerical errors, where his claim that there was no influence was ture because some fortunate cancellations happened in the transform. Generally speaking, it is the solution of the PDE on the grid that is important. Therefore truncation error has to be evaluated for the PDE, not for the separate derivatives. The high-order grid transformation also has to be examined with this criterion, though they are qualitied in most cases.

  Reply With Quote

Old   December 7, 2001, 07:42
Default Re: What's the future use for high-order END schem
  #5
Salvador Navarro-Martinez
Guest
 
Posts: n/a
From unsteady inviscid flow with shock present is clear that the latest versions of ENO (WENO,MP-WENO) are highly recomendable. However as you increase the order of the polynomials, you need to increase the order of the usual RK scheme to advance the flow to keep the scheme stable and in some sense coherent, this largely increases your CPU time for complex problems (too much for 3D???). Other approaches as ADERm (Toro and Titarev) seems more promising as they avoid RK.

If you are dealing with viscous flows with shocks interactions involved the thing gets more complex and the highest order usually drops to 4 (even when doing DNS).

  Reply With Quote

Reply

Thread Tools
Display Modes

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 Off
Trackbacks are On
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
flow analysis kmgraju CFX 3 May 26, 2011 05:09
Constant velocity of the material Sas CFX 15 July 13, 2010 08:56
Simulation of a single bubble with a VOF-method Suzzn CFX 18 October 2, 2009 04:18
Has anyone successfully used transition modell..p2 PetrK CFX 12 May 26, 2006 16:27
particle tracking mike CFX 3 April 17, 2006 00:05


All times are GMT -4. The time now is 12:13.