The Cartesian grid active flux method: linear stability and bound preserving limiting

DOI10.1016/j.amc.2020.125501zbMath1474.65309OpenAlexW3102632308MaRDI QIDQ2662585

Christiane Helzel, Erik Chudzik, David Kerkmann

Publication date: 14 April 2021

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2020.125501

zbMATH Keywords

linear stabilityhyperbolic conservation lawslimitingCartesian grid active flux methodthird order finite volume method

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Hyperbolic conservation laws (35L65) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Hydro- and aero-acoustics (76Q05) Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs (65M25) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

Related Items (7)

Hyperbolic balance laws: modeling, analysis, and numerics. Abstracts from the workshop held February 28 -- March 6, 2021 (hybrid meeting) ⋮ Hyperbolic Balance Laws: Residual Distribution, Local and Global Fluxes ⋮ Extensions of Active Flux to arbitrary order of accuracy ⋮ The Cartesian grid active flux method with adaptive mesh refinement ⋮ A Review of Cartesian Grid Active Flux Methods for Hyperbolic Conservation Laws ⋮ Implicit active flux methods for linear advection ⋮ Active flux methods for hyperbolic systems using the method of bicharacteristics

Cites Work

• Is discontinuous reconstruction really a good idea?
• A new ADER method inspired by the active flux method
• The active flux scheme on Cartesian grids and its low Mach number limit
• Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments
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