Math @ Duke

Publications [#246951] of JianGuo Liu
Papers Published
 Wang, C; Liu, JG, Positivity property of secondorder fluxsplitting schemes for the compressible Euler equations,
Discrete and Continuous Dynamical Systems  Series B, vol. 3 no. 2
(2003),
pp. 201228
(last updated on 2018/03/16)
Abstract: A class of upwind flux splitting methods in the Euler equations of compressible flow is 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 matrices are either symmetric or symmetrizable and keep only nonnegative and nonpositive eigenvalues. That leads to the conclusion that the first order schemes are positive in the sense of LaxLiu [18], which implies that it is L2 stable in some suitable sense. Moreover, the second order scheme is a stable perturbation of the first order scheme, so that the positivity of the second order schemes is also established, under a CFLlike condition. In addition, these splitting methods preserve the positivity of density and energy.


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