5 papers
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…
A generalized Active Flux method of arbitrarily high order in two dimensions
Wasilij Barsukow, Praveen Chandrashekar, Christian Klingenberg +1
The Active Flux method can be seen as an extended finite volume method. The degrees of freedom of this method are cell averages, as in finite volume methods, and in addition shared…
Analysis of the multi-dimensional semi-discrete Active Flux method using the Fourier transform
Wasilij Barsukow, Janina Kern, Christian Klingenberg +1
The degrees of freedom of Active Flux are cell averages and point values along the cell boundaries. These latter are shared between neighbouring cells, which gives rise to a global…
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…