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• W2095239504 abstract "A class of upwind flux splitting methods in theEuler equations of compressible flowis considered in this paper. Using the property that Euler flux $F(U)$is a homogeneous function of degree one in $U$,we reformulate the splitting fluxes with $F^{+}=A^{+} U$,$F^{-}=A^{-} U$, and the corresponding matricesare either symmetric or symmetrizable and keep onlynon-negative and non-positive eigenvalues.That leads to the conclusion that the first order schemesare positive in the sense of Lax-Liu [18],which implies that it is $L^2$-stablein some suitable sense. Moreover, the second order schemeis a stable perturbation of the first order scheme,so that the positivity of the second order schemesis also established, undera CFL-like condition. In addition, these splitting methods preservethe positivity of density and energy." @default.
• W2095239504 created "2016-06-24" @default.
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• W2095239504 date "2003-01-01" @default.
• W2095239504 modified "2023-09-27" @default.
• W2095239504 title "Positivity property of second-order flux-splitting schemes for the compressible Euler equations" @default.
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• W2095239504 doi "https://doi.org/10.3934/dcdsb.2003.3.201" @default.
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