6 papers · 1 filter
A compact fourth-order doubly conservative active flux method with maximum-principle-preserving limiting for degenerate convection--diffusion equations
Junming Duan
The active flux (AF) method is a compact high-order finite volume method originally proposed for solving hyperbolic conservation laws, that evolves cell averages together with poin…
An asymptotic-preserving active flux scheme for the hyperbolic heat equation in the diffusive scaling
Junming Duan, Wasilij Barsukow, Christian Klingenberg
The Active Flux (AF) method is a compact, high-order finite volume scheme that enhances flexibility by introducing point values at cell interfaces as additional degrees of freedom…
Active flux for ideal magnetohydrodynamics: A positivity-preserving scheme with the Godunov-Powell source term
Junming Duan, Praveen Chandrashekar, Christian Klingenberg
The Active Flux (AF) is a compact, high-order finite volume scheme that allows more flexibility by introducing additional point value degrees of freedom at cell interfaces. This pa…
Active flux methods for hyperbolic conservation laws -- flux vector splitting and bound-preservation
Junming Duan, Wasilij Barsukow, Christian Klingenberg
The active flux (AF) method is a compact high-order finite volume method that simultaneously evolves cell averages and point values at cell interfaces. Within the method of lines f…
Active flux methods for hyperbolic conservation laws -- flux vector splitting and bound-preservation: Two-dimensional case
Junming Duan, Wasilij Barsukow, Christian Klingenberg
This paper studies the active flux (AF) methods for two-dimensional hyperbolic conservation laws, focusing on the flux vector splitting (FVS) for the point value update and bound-p…
Active flux methods for hyperbolic conservation laws -- flux vector splitting and bound-preservation: One-dimensional case
Junming Duan, Wasilij Barsukow, Christian Klingenberg
The active flux (AF) method is a compact high-order finite volume method that evolves cell averages and point values at cell interfaces independently. Within the method of lines fr…