Abstract

A new discretization method for hyperbolic systems with stiff relaxation source terms (hyperbolic-relaxation equations) is introduced. The method is based on Huynh’s “upwind moment scheme” for hyperbolic conservation laws with implicit treatment of the source term. A Von Neumann analysis shows superiority in both stability and accuracy of the resulting fully discrete scheme over the method-of-line based semi-discrete schemes, and numerical experiments confirm the analysis. Our goal is developing a unified numerical method for simulating a continuum and transitional flow.

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