ON POSITIVITY OF A CLASS OF FLUX-VECTOR SPLITTING METHODS I. EXPLICIT DIFFERENCE SCHEMES
一类通矢量分裂方法的保正性研究Ⅰ.显式格式

This paper is about the positivity analysis of a class of flux-vector splitting (FVS) methods for the compressible Euler equations, which include gas-kinetic Beam scheme8], Steger-Warming FVS method9], and Lax-Friedrichs scheme. It shows that the density and the internal energy could keep non-negative values under the CFL condition for all above three schemes once the initial gas stays in a physically realizable state. The proof of positivity is closely related to the pseudo-particle representation of FVS schemes.