# Entropy fix for godunov scheme

For non linear system of hyperbolic PDE, The finite volume methods work well (because of inherent conservation). Godunov scheme is a very elegant solution philosophy. For linear system, it is nothing but upwinding, but for nonlinear system, there are entropy issues. Also the Riemann solution at the local Riemann problem can not be determined if the global solution is the centered expansion fan. For this issue, we apply entropy fix. (or local linearisation e.g. Roe's) There are lot of solutions provided for this. Which one gives most consistent and accurate results?

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 In numerical schemes for conservation laws, the conservation property is due to the use of flux-differencing. It has nothing to do with the use of finite volumes; finite difference flux-differencing methods for conservation laws are also conservative. – David Ketcheson Jun 4 '12 at 18:02 As Jed says, you don't need an entropy fix for Godunov's method. Even if you replace the exact Riemann solver with an approximate one, any first-order scheme will typically have so much diffusion that no entropy fix is needed. – David Ketcheson Jun 4 '12 at 18:04 Yes, I today I carefully read RLeVeque's and Toro's books on hyperbolic PDE and numerical methods. I was definitely wrong in my understanding before. @Jed Brown and David Ketcheson, thank you very much. @ myself, I should ask more mature questions which make sense. Thanks again. – Subodh Jun 4 '12 at 18:07 There was nothing wrong with your question, and it's fine to ask basic questions here. But before your question you gave an explanation, and it's true that that part wasn't correct. Perhaps you could revise the question now that you understand, in order to make it more useful. – David Ketcheson Jun 4 '12 at 18:13