9 citations · 9 across the 15 of their papers we have counts for
16 papers
A compact high-order and positivity-preserving active flux method for compressible Navier--Stokes equations on Cartesian meshes
Junming Duan, Wasilij Barsukow, Christian Klingenberg
This paper develops a compact fourth-order positivity-preserving active flux (AF) method for the one- and two-dimensional compressible Navier--Stokes equations on Cartesian meshes.…
Semi-discrete Active Flux method for two-dimensional hyperbolic systems with Coriolis source terms
Nikhil Manoj, Wasilij Barsukow, Christian Klingenberg
We investigate the semi-discrete Active Flux numerical method on Cartesian grids applied to two-dimensional linear and nonlinear shallow water equations with Coriolis source terms.…
On Enhancing the Dissipative Behavior of Active Flux Advection Schemes
Christian Klingenberg, Simon Krotsch, Philip Roe
In this work, the traditional third-order Active Flux advection scheme is modified by reformulating the method and introducing additional parameters. The effect of these parameters…
On the equivalence of semi-discrete Active Flux and Discontinuous Galerkin methods and a comparison of their performance
Wasilij Barsukow, Christian Klingenberg, Simon Krotsch
The Active Flux (AF) method employs a globally continuous approximation, like continuous Finite Element methods. This is achieved through the placement of point values at cell inte…
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…
Stability of the Active Flux Method in the Framework of Summation-by-Parts Operators
Wasilij Barsukow, Christian Klingenberg, Lisa Lechner +3
The Active Flux method is a numerical method for conservation laws using a combination of cell averages and point values as independent degrees of freedom, based on ideas from fini…
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…
Local sensitivity-preserving random data down-sampling for experimental design
Kathrin Hellmuth, Christian Klingenberg, Qin Li
The quality of numerical reconstructions for unknown parameters in inverse problems depends fundamentally on the selection of experimental data. To ensure a robust reconstruction,…
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…
Efficient Numerical Wave Propagation Enhanced By An End-to-End Deep Learning Model
Luis Kaiser, Richard Tsai, Christian Klingenberg
In a variety of scientific and engineering domains, the need for high-fidelity and efficient solutions for high-frequency wave propagation holds great significance. Recent advances…
A semi-discrete Active Flux method for the Euler equations on Cartesian grids
Rémi Abgrall, Wasilij Barsukow, Christian Klingenberg
Active Flux is an extension of the Finite Volume method and additionally incorporates point values located at cell boundaries. This gives rise to a globally continuous approximatio…
Reconstructing the kinetic chemotaxis kernel using macroscopic data: well-posedness and ill-posedness
Kathrin Hellmuth, Christian Klingenberg, Qin Li +1
Bacterial motion is steered by external stimuli (chemotaxis), and the motion described on the mesoscopic scale is uniquely determined by a parameter that models velocity change…