Michael Dumbser
YOU?
Author Swipe
View article: A structure-preserving and thermodynamically compatible cell-centered Lagrangian finite volume scheme for continuum mechanics
A structure-preserving and thermodynamically compatible cell-centered Lagrangian finite volume scheme for continuum mechanics Open
In this work we present a novel structure-preserving scheme for the discretization of the Godunov-Peshkov-Romenski (GPR) model of continuum mechanics written in Lagrangian form. This model admits an extra conservation law for the total ene…
View article: On general and complete multidimensional Riemann solvers for nonlinear systems of hyperbolic conservation laws
On general and complete multidimensional Riemann solvers for nonlinear systems of hyperbolic conservation laws Open
In this work, we introduce a framework to design multidimensional Riemann solvers for nonlinear systems of hyperbolic conservation laws on general unstructured polygonal Voronoi-like tessellations. In this framework we propose two simple b…
View article: A new first-order formulation of the Einstein equations: comparison among different high order numerical schemes
A new first-order formulation of the Einstein equations: comparison among different high order numerical schemes Open
The solution of the Einstein-Euler equations by the majority of numerical codes is still based on traditional finite difference schemes for the Einstein sector, while it relies on conservative schemes for the matter part. This is due to th…
View article: Variational derivation and compatible discretizations of the Maxwell-GLM system
Variational derivation and compatible discretizations of the Maxwell-GLM system Open
We present a novel variational derivation of the Maxwell-GLM system, which augments the original vacuum Maxwell equations via a generalized Lagrangian multiplier approach (GLM) by adding two supplementary acoustic subsystems and which was …
View article: Well-balanced High-order Finite Difference Weighted Essentially Nonoscillatory Schemes for a First-order Z4 Formulation of the Einstein Field Equations
Well-balanced High-order Finite Difference Weighted Essentially Nonoscillatory Schemes for a First-order Z4 Formulation of the Einstein Field Equations Open
We develop a new class of high-order accurate well-balanced finite difference (FD) weighted essentially nonoscillatory (WENO) methods for numerical general relativity (GR), which can be applied to any first-order reduction of the Einstein …
View article: A first-order hyperbolic reformulation of the Cahn-Hilliard equation
A first-order hyperbolic reformulation of the Cahn-Hilliard equation Open
In this paper we present a new first-order hyperbolic reformulation of the Cahn-Hilliard equation. The model is obtained from the combination of augmented Lagrangian techniques proposed earlier by the authors of this paper, with a classica…
View article: High-order discontinuous Galerkin schemes with subcell finite volume limiter and adaptive mesh refinement for a monolithic first-order BSSNOK formulation of the Einstein-Euler equations
High-order discontinuous Galerkin schemes with subcell finite volume limiter and adaptive mesh refinement for a monolithic first-order BSSNOK formulation of the Einstein-Euler equations Open
We propose a high order discontinuous Galerkin (DG) scheme with subcell finite volume (FV) limiter to solve a monolithic first--order hyperbolic BSSNOK formulation of the coupled Einstein--Euler equations. The numerical scheme runs with ad…
View article: A monolithic first--order BSSNOK formulation of the Einstein--Euler equations and its solution with path-conservative finite difference CWENO schemes
A monolithic first--order BSSNOK formulation of the Einstein--Euler equations and its solution with path-conservative finite difference CWENO schemes Open
We present a new, monolithic first--order (both in time and space) BSSNOK formulation of the coupled Einstein--Euler equations. The entire system of hyperbolic PDEs is solved in a completely unified manner via one single numerical scheme a…
View article: A Semi-implicit Finite Volume Scheme for Incompressible Two-Phase Flows
A Semi-implicit Finite Volume Scheme for Incompressible Two-Phase Flows Open
This paper presents a mass and momentum conservative semi-implicit finite volume (FV) scheme for complex non-hydrostatic free surface flows, interacting with moving solid obstacles. A simplified incompressible Baer-Nunziato type model is c…
View article: An all Mach number semi-implicit hybrid Finite Volume/Virtual Element method for compressible viscous flows on Voronoi meshes
An all Mach number semi-implicit hybrid Finite Volume/Virtual Element method for compressible viscous flows on Voronoi meshes Open
We present a novel high order semi-implicit hybrid finite volume/virtual element numerical scheme for the solution of compressible flows on Voronoi tessellations. The method relies on the flux splitting of the compressible Navier-Stokes eq…
View article: A unified SHTC multiphase model of continuum mechanics
A unified SHTC multiphase model of continuum mechanics Open
In this paper, we present a unified nonequilibrium model of continuum mechanics for compressible multiphase flows. The model, which is formulated within the framework of Symmetric Hyperbolic Thermodynamically Compatible (SHTC) equations, c…
View article: An exactly curl-free finite-volume scheme for a hyperbolic compressible barotropic two-phase model
An exactly curl-free finite-volume scheme for a hyperbolic compressible barotropic two-phase model Open
We present a new second order accurate structure-preserving finite volume scheme for the solution of the compressible barotropic two-phase model of Romenski et. al in multiple space dimensions. The governing equations fall into the wider c…
View article: A divergence-free hybrid finite volume / finite element scheme for the incompressible MHD equations based on compatible finite element spaces with a posteriori limiting
A divergence-free hybrid finite volume / finite element scheme for the incompressible MHD equations based on compatible finite element spaces with a posteriori limiting Open
We present a novel semi-implicit hybrid finite volume/finite element (FV/FE) method for the equations of viscous and resistive incompressible magnetohydrodynamics (MHD). The scheme preserves the divergence-free property of the magnetic fie…
View article: A New Class of Simple, General and Efficient Finite Volume Schemes for Overdetermined Thermodynamically Compatible Hyperbolic Systems
A New Class of Simple, General and Efficient Finite Volume Schemes for Overdetermined Thermodynamically Compatible Hyperbolic Systems Open
In this paper, a new efficient, and at the same time, very simple and general class of thermodynamically compatible finite volume schemes is introduced for the discretization of nonlinear, overdetermined, and thermodynamically compatible f…
View article: A well-balanced and exactly divergence-free staggered semi-implicit hybrid finite volume / finite element scheme for the incompressible MHD equations
A well-balanced and exactly divergence-free staggered semi-implicit hybrid finite volume / finite element scheme for the incompressible MHD equations Open
We present a new exactly divergence-free and well-balanced hybrid finite volume/finite element scheme for the numerical solution of the incompressible viscous and resistive magnetohydrodynamics (MHD) equations on staggered unstructured mix…
View article: A new thermodynamically compatible finite volume scheme for Lagrangian gas dynamics
A new thermodynamically compatible finite volume scheme for Lagrangian gas dynamics Open
The equations of Lagrangian gas dynamics fall into the larger class of overdetermined hyperbolic and thermodynamically compatible (HTC) systems of partial differential equations. They satisfy an entropy inequality (second principle of ther…
View article: High-order ADER Discontinuous Galerkin schemes for a symmetric hyperbolic model of compressible barotropic two-fluid flows
High-order ADER Discontinuous Galerkin schemes for a symmetric hyperbolic model of compressible barotropic two-fluid flows Open
This paper presents a high-order discontinuous Galerkin finite element method to solve the barotropic version of the conservative symmetric hyperbolic and thermodynamically compatible (SHTC) model of compressible two-phase flow, introduced…
View article: A well-balanced and exactly divergence-free staggered semi-implicit hybrid finite volume/finite element scheme for the incompressible MHD equations
A well-balanced and exactly divergence-free staggered semi-implicit hybrid finite volume/finite element scheme for the incompressible MHD equations Open
We present a new divergence-free and well-balanced hybrid FV/FE scheme for the incompressible viscous and resistive MHD equations on unstructured mixed-element meshes in 2 and 3 space dimensions. The equations are split into subsystems. Th…
View article: A New Thermodynamically Compatible Finite Volume Scheme for Magnetohydrodynamics
A New Thermodynamically Compatible Finite Volume Scheme for Magnetohydrodynamics Open
In this paper we propose a novel thermodynamically compatible finite volume\nscheme for the numerical solution of the equations of magnetohydrodynamics\n(MHD) in one and two space dimensions. As shown by Godunov in 1972, the MHD\nsystem ca…
View article: An implicit staggered hybrid finite volume/finite element solver for the incompressible Navier-Stokes equations
An implicit staggered hybrid finite volume/finite element solver for the incompressible Navier-Stokes equations Open
We present a novel fully implicit hybrid finite volume/finite element method for incompressible flows. Following previous works on semi-implicit hybrid FV/FE schemes, the incompressible Navier-Stokes equations are split into a pressure and…