Abstract
Hyperbolic conservation law equations and convection-dominated
convection-diffusion equations can be solved numerically using
high-order weighted essentially non-oscillatory (WENO) techniques in
computational fluid mechanics. In this paper, we extend the modified
WENO scheme to mixed-type equations. Numerical examples for the van der
Waals equations and the corresponding viscosity-capillarity equations
are presented to illustrate the efficiency and structure of our
algorithm. The emphasis is on the Riemann problem of mixed equations
under different pressure states.