21 citations · 41 across the 30 of their papers we have counts for
35 papers
A TVD Active Flux method for scalar conservation laws
Wasilij Barsukow
Focusing on scalar conservation laws, a TVD theory is developed for the fully discrete, single-stage Active Flux method. The classical choice of degrees of freedom is considered, y…
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 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…
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…
Stationarity preserving nodal Finite Element methods for multi-dimensional linear hyperbolic balance laws via a Global Flux quadrature formulation
Wasilij Barsukow, Mario Ricchiuto, Davide Torlo
We consider linear, hyperbolic systems of balance laws in several space dimensions. They possess non-trivial steady states, which result from the equilibrium between derivatives of…