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math.NA2025
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…
math.NA2025
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…
math.NA2025
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…