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September 4, 2011, 16:43 
3rdorder upwind, flux formulation for limiter

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September 5, 2011, 09:57 

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Quote:
F=0.5[F+Fabs(F/u)(uu)] The left uL and right state uR can be defined as u=u0.25(r)[(1k)(uu)+(1+k)(uu)] u=u+0.25(r)[(1k)(uu)+(1+k)(uu)] 

September 5, 2011, 17:58 

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Thanks a lot for your explanation!
Is that the same approach as KurganovTadamor scheme from MUSCL's page in wikipedia? It is totally unclear for me how to calculate this () Probably because I don't clearly get what is F for me. As far as i understand for incompressible convection problem I have equation and equation, where . From that i derive (linearized) form of the convection operator (for 1st component) where is fixed. Now for MUSCL I should consider convection equation in the following form where Then ? Is that it? 

September 6, 2011, 01:20 

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https://www.yousendit.com/download/M...WkJVVGxFQlE9PQ (Vol. 1) https://www.yousendit.com/download/M...UnFRR2RFQlE9PQ (Vol. 2) Also, for more information about Upwind schemes: R. C. Swanson. and E. Turkel "ON CENTRALDIFFERENCE AND UPWIND SCHEMES" ftp://124.42.15.59/ck/201103/165/00...%20schemes.pdf Brain van Lee: "PROGRESS IN MULTIDIMENSIONAL UPWIND DIFFERENCING" http://ntrs.nasa.gov/archive/nasa/ca...1993001620.pdf cheers! Last edited by congtuha; September 6, 2011 at 03:50. 

September 6, 2011, 05:52 

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September 6, 2011, 07:20 

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It is easy to construct your numerical solution with this scheme. However if you dealt with the boundary layer, the boundary layer seems too big. To improve the accuracy, you should use matrix dissipation I have tested the upwind MUSCL type and upwind NONMUSCL type (say TVD scheme  see the Reference below!) with various limiter functions for linear advection equations and inviscid Burgers’ equation. (If you are interested in these comparisons just past your email address here). Limiter functions play the key role for upwind schemes. Be careful with the choice of limiter function! You might get nonphysical results if you do not pick up the suitable limiter for your problem. I also applied the upwind MUSCL type and upwind TVD to the solution of RANS for twophase and threephase mixture flows. The upwind TVD with limiter 9d (see ref.) gave the best accuracy and numerical stability. I can only share some of my experience on the upwind scheme here. I hope it help for your choice. Cheers! Ref. Yeeh et al. “HighResolution ShockCapturing Schemes for Inviscid and Viscous Hypersonic Flows” http://ntrs.nasa.gov/archive/nasa/ca...1988013267.pdf Last edited by congtuha; September 6, 2011 at 14:10. 

September 6, 2011, 15:41 

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Yes, interested! Thanks a lot, really appreciate your help!
кirill.terehоv@gмail.сом Last edited by carambula; September 9, 2011 at 18:07. 

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