Positivity-Preserving Analysis of Explicit and Implicit Lax–Friedrichs Schemes for Compressible Euler Equations

Authors:
Hua-Zhong Tang;Kun Xu
Affiliations:
State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100080, People's Republic of China; makxu@uxmail.ust.hk
Venue:
Journal of Scientific Computing
Year:
2000

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Abstract

This paper presents the positivity analysis of the explicit and implicit Lax–Friedrichs (LxF) schemes for the compressible Euler equations. The theoretical proof is closely based on the decomposition of fluid variables and their corresponding fluxes into the pseudo-particles representation. For both explicit and implicit 1st-order LxF schemes, from any initial realizable state the density and the internal energy could keep non-negative values under the CFL condition with Courant number 1.