A Review of Cartesian Grid Active Flux Methods for Hyperbolic Conservation Laws

DOI10.1007/978-3-031-40864-9_6zbMath1529.65034OpenAlexW4387225028MaRDI QIDQ6182844

Erik Chudzik, Christiane Helzel

Publication date: 22 December 2023

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-031-40864-9_6

zbMATH Keywords

hyperbolic conservation lawsactive flux methods

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) Finite volume methods for boundary value problems involving PDEs (65N08)

Cites Work

• Unnamed Item
• Positivity-preserving method for high-order conservative schemes solving compressible Euler equations
• Is discontinuous reconstruction really a good idea?
• Finite volume evolution Galerkin methods for nonlinear hyperbolic systems.
• Designing CFD methods for bandwidth -- a physical approach
• The active flux scheme for nonlinear problems
• A new ADER method inspired by the active flux method
• The active flux scheme on Cartesian grids and its low Mach number limit
• The Cartesian grid active flux method: linear stability and bound preserving limiting
• A combination of residual distribution and the active flux formulations or a new class of schemes that can combine several writings of the same hyperbolic problem: application to the 1D Euler equations
• Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments
• On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly consistent mass matrix. Part 2: Implementation
• Evolution Galerkin methods for hyperbolic systems in two space dimensions
• A Simple Explanation of Superconvergence for Discontinuous Galerkin Solutions to u_t+u_x=0
• Extensions of Active Flux to arbitrary order of accuracy
• The Cartesian grid active flux method with adaptive mesh refinement

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