Wasilij Barsukow
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View article: Stationarity preserving nodal Finite Element methods for multi-dimensional linear hyperbolic balance laws via a Global Flux quadrature formulation
Stationarity preserving nodal Finite Element methods for multi-dimensional linear hyperbolic balance laws via a Global Flux quadrature formulation Open
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 the unknowns in different directions, and the sources. Sta…
View article: Semi-discrete Active Flux as a Petrov-Galerkin method
Semi-discrete Active Flux as a Petrov-Galerkin method Open
Active Flux (AF) is a recent numerical method for hyperbolic conservation laws, whose degrees of freedom are averages/moments and (shared) point values at cell interfaces. It has been noted previously in a heuristic fashion that it thus co…
View article: An asymptotic-preserving active flux scheme for the hyperbolic heat equation in the diffusive scaling
An asymptotic-preserving active flux scheme for the hyperbolic heat equation in the diffusive scaling Open
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 alongside cell averages. The method of lines is employed he…
View article: Stability of the Active Flux Method in the Framework of Summation-by-Parts Operators
Stability of the Active Flux Method in the Framework of Summation-by-Parts Operators Open
The Active Flux method is a numerical method for conservation laws using a combination of cell averages and point values, based on ideas from finite volumes and finite differences. This unusual mix has been shown to work well in many situa…
View article: An Arbitrarily High-Order Fully Well-balanced Hybrid Finite Element–Finite Volume Method for a One-dimensional Blood Flow Model
An Arbitrarily High-Order Fully Well-balanced Hybrid Finite Element–Finite Volume Method for a One-dimensional Blood Flow Model Open
We propose an arbitrarily high-order accurate, fully well-balanced numerical method for the one-dimensional blood flow model. The developed method employs a continuous solution representation, combining conservative and primitive formulati…
View article: Genuinely multi-dimensional stationarity preserving Finite Volume formulation for nonlinear hyperbolic PDEs
Genuinely multi-dimensional stationarity preserving Finite Volume formulation for nonlinear hyperbolic PDEs Open
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 in different directions. Such methods therefore ignore a pos…
View article: An Active Flux method for the Euler equations based on the exact acoustic evolution operator
An Active Flux method for the Euler equations based on the exact acoustic evolution operator Open
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 locally linearized manner by using the exact evolution operato…
View article: A generalized Active Flux method of arbitrarily high order in two dimensions
A generalized Active Flux method of arbitrarily high order in two dimensions Open
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 point values at the cell interfaces, giving rise to a glob…
View article: Structure Preserving Nodal Continuous Finite Elements via Global Flux Quadrature
Structure Preserving Nodal Continuous Finite Elements via Global Flux Quadrature Open
Numerical methods for hyperbolic PDEs require stabilization. For linear acoustics, divergence‐free vector fields should remain stationary, but classical Finite Difference methods add incompatible diffusion that dramatically restricts the s…
View article: Analysis of the multi-dimensional semi-discrete Active Flux method using the Fourier transform
Analysis of the multi-dimensional semi-discrete Active Flux method using the Fourier transform Open
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 globally continuous reconstruction. The semi-discrete Active Flux…
View article: Active flux methods for hyperbolic conservation laws -- flux vector splitting and bound-preservation
Active flux methods for hyperbolic conservation laws -- flux vector splitting and bound-preservation Open
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 framework, the existing Jacobian splitting-based point value…
View article: A node-conservative vorticity-preserving Finite Volume method for linear acoustics on unstructured grids
A node-conservative vorticity-preserving Finite Volume method for linear acoustics on unstructured grids Open
Instead of ensuring that fluxes across edges add up to zero, we split the edge in two halves and also associate different fluxes to each of its sides. This is possible due to non-standard Riemann solvers with free parameters. We then enfor…
View article: Active flux methods for hyperbolic conservation laws -- flux vector splitting and bound-preservation: Two-dimensional case
Active flux methods for hyperbolic conservation laws -- flux vector splitting and bound-preservation: Two-dimensional case Open
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-preserving (BP) limitings, which is an extension of our prev…
View article: Structure preserving nodal continuous Finite Elements via Global Flux quadrature
Structure preserving nodal continuous Finite Elements via Global Flux quadrature Open
Numerical methods for hyperbolic PDEs require stabilization. For linear acoustics, divergence-free vector fields should remain stationary, but classical Finite Difference methods add incompatible diffusion that dramatically restricts the s…
View article: An asymptotic-preserving multidimensionality-aware finite volume numerical scheme for Euler equations
An asymptotic-preserving multidimensionality-aware finite volume numerical scheme for Euler equations Open
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View article: Active flux methods for hyperbolic conservation laws -- flux vector splitting and bound-preservation: One-dimensional case
Active flux methods for hyperbolic conservation laws -- flux vector splitting and bound-preservation: One-dimensional case Open
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 framework, the point value can be updated based on Jacobian s…
View article: Performance of high-order Godunov-type methods in simulations of astrophysical low Mach number flows
Performance of high-order Godunov-type methods in simulations of astrophysical low Mach number flows Open
High-order Godunov methods for gas dynamics have become a standard tool for simulating different classes of astrophysical flows. Their accuracy is mostly determined by the spatial interpolant used to reconstruct the pair of Riemann states …
View article: Performance of high-order Godunov-type methods in simulations of astrophysical low Mach number flows
Performance of high-order Godunov-type methods in simulations of astrophysical low Mach number flows Open
Supplementary materials for the paper "Performance of high-order Godunov-type methods in simulations of astrophysical low Mach number flows". The supplementary materials are split into two .zip archives (KH2D-plots.zip and 3D-TURBULENCE-WA…
View article: Performance of high-order Godunov-type methods in simulations of astrophysical low Mach number flows
Performance of high-order Godunov-type methods in simulations of astrophysical low Mach number flows Open
Supplementary materials for the paper "Performance of high-order Godunov-type methods in simulations of astrophysical low Mach number flows". The supplementary materials are split into two .zip archives (KH2D-plots.zip and 3D-TURBULENCE-WA…
View article: A semi-discrete Active Flux method for the Euler equations on Cartesian grids
A semi-discrete Active Flux method for the Euler equations on Cartesian grids Open
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 approximation of the solution. Originally, the Active Flux method emerg…
View article: Truly multi-dimensional all-speed methods for the Euler equations
Truly multi-dimensional all-speed methods for the Euler equations Open
Several recent all-speed time-explicit numerical methods for the Euler equations on Cartesian grids are presented and their properties assessed experimentally on a complex application. These methods are truly multi-dimensional, i.e. the fl…
View article: Implicit Active Flux methods for linear advection
Implicit Active Flux methods for linear advection Open
In this work we develop implicit Active Flux schemes for the scalar advection equation. At every cell interface we approximate the solution by a polynomial in time. This allows to evolve the point values using characteristics and to update…
View article: All-speed numerical methods for the Euler equations via a sequential explicit time integration
All-speed numerical methods for the Euler equations via a sequential explicit time integration Open
This paper presents a new strategy to deal with the excessive diffusion that standard finite volume methods for compressible Euler equations display in the limit of low Mach number. The strategy can be understood as using centered discreti…
View article: Extensions of Active Flux to arbitrary order of accuracy
Extensions of Active Flux to arbitrary order of accuracy Open
Active Flux is a recently developed numerical method for hyperbolic conservation laws. Its classical degrees of freedom are cell averages and point values at cell interfaces. These latter are shared between adjacent cells, leading to a glo…
View article: A well-balanced Active Flux method for the shallow water equations with wetting and drying
A well-balanced Active Flux method for the shallow water equations with wetting and drying Open
Active Flux is a third order accurate numerical method which evolves cell averages and point values at cell interfaces independently. It naturally uses a continuous reconstruction, but is stable when applied to hyperbolic problems. In this…