The Cartesian Grid Active Flux Method: Linear stability and bound preserving limiting

Erik Chudzik, Christiane Helzel and David Kerkmann

Applied Mathematics and Computation, 2021, vol. 393, issue C

Abstract: The primary contribution of this article is a linear stability analysis of the two-dimensional Cartesian grid Active Flux method. For the advection equation we show that stability for CFL ≤ 1 requires a more accurate flux computation than previously assumed. For the acoustic equations we confirm the expected stability for CFL≤12. Furthermore, we introduce a nonlinear limiting based on a bound preserving multi-dimensional reconstruction. Numerical results for advection and Burgers’ equation illustrate the performance of this limiting technique.

Keywords: Cartesian grid Active Flux method; Third order finite volume method; Hyperbolic conservation laws; Linear stability; limiting (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:393:y:2021:i:c:s0096300320304598

DOI: 10.1016/j.amc.2020.125501

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