Active flux methods for hyperbolic systems using the method of bicharacteristics
DOI10.1007/s10915-024-02462-zOpenAlexW4392375572MaRDI QIDQ6196230
Mária Lukáčová-Medvid'ová, Erik Chudzik, Christiane Helzel
Publication date: 14 March 2024
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10915-024-02462-z
Euler equationslinear hyperbolic systemsmethod of bicharacteristicsCartesian grid active flux method
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 difference methods for boundary value problems involving PDEs (65N06) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Maxwell equations (35Q61) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) Euler equations (35Q31)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On evolution Galerkin methods for the Maxwell and the linearized Euler equations.
- Towards the ultimate conservative difference scheme. IV: A new approach to numerical convection
- Is discontinuous reconstruction really a good idea?
- An evolution Galerkin scheme for the shallow water magnetohydrodynamic equations in two space dimensions
- 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
- A fourth-order auxiliary variable projection method for zero-Mach number gas dynamics
- 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
- 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
- The numerical solution of hyperbolic systems of partial differential equations in three independent variables
- Numerical Solution of the Riemann Problem for Two-Dimensional Gas Dynamics
- Comparison of Several Difference Schemes on 1D and 2D Test Problems for the Euler Equations
- Third order finite volume evolution Galerkin (FVEG) methods for two-dimensional wave equation system
- Evolution Galerkin methods for hyperbolic systems in two space dimensions
- Finite Volume Evolution Galerkin Methods for Hyperbolic Systems
- Extensions of Active Flux to arbitrary order of accuracy
- The Cartesian grid active flux method with adaptive mesh refinement
