# ROE-flux difference splitting

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 January 27, 2002, 09:44 ROE-flux difference splitting #1 duanyee Guest   Posts: n/a Now I meet with some difficulties in Roe-avarage flux difference splitting solving the fluxs.At sonic points there is wrong entropy pionts.so I have to fix the entropy in Roe scheme.but I don't know how to modify it in the vector systems .ie.for Euler Equations.please give me the method in details.thank you very much !!

 February 1, 2002, 04:06 Re: ROE-flux difference splitting #2 Samuel KOKH Guest   Posts: n/a If I have correctly understood your problem, a possible answer might be to add a perturbation to absolute values of the jacobian matrix eigenvalues. Namely, lambda being such eigenvalue, instead of using |lambda|, replace it with sqrt[(1+epsilon)*lambda^2], epsilon being a small parameter you can tune accordingly to your needs.

 February 1, 2002, 05:59 Re: ROE-flux difference splitting #3 Sandro Guest   Posts: n/a I think you could also use the Harten and Hyman Entropy fix. You use for |lambda| = max ( |lambda| , eps) where eps = max (0 , (lambda(i+1/2)-lambda(i) , (lambda(i+1)- lambda(i+1/2) ) So you only use the correction on expansion shocks and not on compression shocks. Sandro

 February 2, 2002, 00:36 Re: ROE-flux difference splitting #4 duanyee Guest   Posts: n/a Thank you very much I still can't undeerstand the relationship between roe characteristic speed and eiginvalues of Jacobian in the hypobolic conservative systems.for example 1) lamda = f'(u) ??? 2) lamda1

 February 2, 2002, 00:38 Re: ROE-flux difference splitting #5 duanyee Guest   Posts: n/a

 February 2, 2002, 12:09 Re: ROE-flux difference splitting #6 Samuel KOKH Guest   Posts: n/a You are absolutely right. However I just intended to sketch a simple mean to fulfil the thread purpose. I hope I haven't confused anyone with my previous post. The entropy fix problem is always annoying as, as far as I know, there's no "ultimate entropy fix user guide" around. If anyone has a nice reference, just let me know.