A new boundary asymptotic-preserving upwind scheme captures equilibrium limits and boundary-layer jumps for hyperbolic relaxation IBVPs, with a unified treatment of interface problems where the relaxation time is discontinuous.
Asymptotic-preserving schemes for the initial-boundary value problem of hyperbolic relaxation systems
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abstract
In this work, we present a numerical method for the initial-boundary value problem (IBVP) of first-order hyperbolic systems with source terms. The scheme directly solves the relaxation system using a relatively coarse mesh and captures the equilibrium behavior quite well, even in the presence of boundary layers. This method extends the concept of asymptotic-preserving schemes from initial-value problems to IBVPs. Moreover, we apply this idea to design a unified numerical scheme for the interface problem of relaxation systems.
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Asymptotic-preserving schemes for the initial-boundary value problem of hyperbolic relaxation systems
A new boundary asymptotic-preserving upwind scheme captures equilibrium limits and boundary-layer jumps for hyperbolic relaxation IBVPs, with a unified treatment of interface problems where the relaxation time is discontinuous.