High-Order Polynomial Expansions (HOPE) for flux-vector splitting

The Van Leer flux splitting is known to produce excessive numerical dissipation for Navier-Stokes calculations. Researchers attempt to remedy this deficiency by introducing a higher order polynomial expansion (HOPE) for the mass flux. In addition to Van Leer's splitting, a term is introduced so that the mass diffusion error vanishes at M equals 0. Several splittings for pressure are proposed and examined. The effectiveness of the HOPE scheme is illustrated for 1-D hypersonic conical viscous flow and 2-D supersonic shock-wave boundary layer interactions. Also, the authors give the weakness of the scheme and suggest areas for further investigation