Positivity of flux vector splitting schemes

Over the last ten years, robustness of schemes has raised an increasing int erest among the CFD community. One mathematical aspect of scheme robustness is the positivity preserving property. At high Mach numbers, solving the c onservative Euler equations can lead to negative densities or internal ener gy. Some schemes such as the flux vector splitting (FVS) schemes are known to avoid this drawback. In this study, a general method is detailed to anal yze the positivity of FVS schemes. As an application, three classical FVS s chemes (Van Leer's, Hanel's variant, and Steger and Warming's) are proved t o be positively conservative under a CFL-like condition. Finally, it is pro ved that for any FVS scheme, there is an intrinsic incompatibility between the desirable property of positivity and the exact resolution of contact di scontinuities. (C) 1999 Academic Press.