Pseudoparticle representation and positivity analysis of explicit and implicit Steger-Warming FVS schemes
This paper is about the pseudo-particle representation and the positivity analysis of an explicit and an implicit Steger and Warming's flux vector splitting (FVS) scheme for the compressible Euler equations. The positivity proof is based on the motion of pseudo-particles. For the explicit scheme, it shows that the density and the internal energy could keep non-negative values under the CFL-like condition for the Steger-Warming FVS scheme once the initial gas stays in a physically realizable state. For the implicit method, under a stronger CFL-like condition, the positivity property can also be preserved.