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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.
Liu et al. (Tue,) studied this question.
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