The paper presents new active flux (AF) methods for solving hyperbolic conservation laws, with a focus on ensuring bound-preserving (BP) properties of the numerical solutions. The key contributions are:
Flux vector splitting (FVS) is used for the point value update, which provides a natural and uniform remedy to the transonic issue encountered in previous Jacobian splitting-based AF methods.
Convex limiting approaches are developed for the cell average update to preserve global or local bounds, such as the maximum principle for scalar conservation laws and positivity of density and pressure for the compressible Euler equations.
A scaling limiter is applied to the point value update to further enforce the BP property.
The paper demonstrates the accuracy, BP properties, and shock-capturing ability of the proposed methods through various challenging benchmark tests, including the LeBlanc and double rarefaction Riemann problems, the Sedov point blast wave, and blast wave interaction problems.
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by Junming Duan... a las arxiv.org 05-07-2024
https://arxiv.org/pdf/2405.02447.pdfConsultas más profundas