Abstract
AbstractWe present the first implementation of the Active Flux method on adaptively refined Cartesian grids. The Active Flux method is a third order accurate finite volume method for hyperbolic conservation laws, which is based on the use of point values as well as cell average values of the conserved quantities. The resulting method has a compact stencil in space and time and good stability properties. The method is implemented as a new solver in ForestClaw, a software for parallel adaptive mesh refinement of patch-based solvers. On each Cartesian grid patch the single grid Active Flux method can be applied. The exchange of data between grid patches is organised via ghost cells. The local stencil in space and time and the availability of the point values that are used for the reconstruction, leads to an efficient implementation. The resulting method is third order accurate, conservative and allows the use of subcycling in time.
Funder
Defense Sciences Office, DARPA
Publisher
Springer Science and Business Media LLC
Subject
Computational Theory and Mathematics,General Engineering,Theoretical Computer Science,Software,Applied Mathematics,Computational Mathematics,Numerical Analysis
Reference27 articles.
1. Barsukow, W.: Low mach number finite volume methods for the acoustic and euler equations. Doctoral thesis, Universität Würzburg (2018)
2. Barsukow, W.: Stationarity preservation properties of the active flux scheme on cartesian grids. Commun. Appl. Comput. (2020)
3. Barsukow, W.: The Active Flux scheme for nonlinear problems. J. Sci. Comput. 86(3), 1–34 (2021)
4. Barsukow, W., Berberich, J.P., Klingenberg, C.: On the active flux scheme for hyperbolic PDEs with source terms. SIAM J. Sci. Comput. 43, A4015–A4042 (2021)
5. Barsukow, W., Hohm, J., Klingenberg, C., Roe, P.L.: The active flux scheme on Cartesian grids and its low Mach number limit. J. Sci. Comput. 81(1), 594–622 (2019)
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献