13 papers
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…
An Active Flux method for the Euler equations based on the exact acoustic evolution operator
Wasilij Barsukow
A new Active Flux method for the multi-dimensional Euler equations is based on an additive operator splitting into acoustics and advection. The acoustic operator is solved in a loc…
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…
Genuinely multi-dimensional stationarity preserving Finite Volume formulation for nonlinear hyperbolic PDEs
Wasilij Barsukow, Mirco Ciallella, Mario Ricchiuto +1
Classical Finite Volume methods for multi-dimensional problems include stabilization (e.g.\ via a Riemann solver), that is derived by considering several one-dimensional problems i…
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…
Stationarity preservation and the low Mach number behaviour of the Discontinuous Galerkin method on Cartesian grids
Wasilij Barsukow
Due to added numerical stabilization (diffusion), the stationary states of numerical methods for hyperbolic problems need not be consistent discretizations of those of the PDEs. A…