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A high-order numerical scheme for the mixed conservation laws
  • Shaoqing Liu,
  • Hongxia Liu
Shaoqing Liu
Taiyuan University of Technology School of Mathematics
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Hongxia Liu
Taiyuan University of Technology School of Information and Computer Science

Corresponding Author:[email protected]

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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.