6 papers
Stability analysis of Arbitrary-Lagrangian-Eulerian ADER-DG methods on classical and degenerate spacetime geometries
Mauro Bonafini, Davide Torlo, Elena Gaburro
In this paper, we present a thorough von Neumann stability analysis of explicit and implicit Arbitrary-Lagrangian-Eulerian (ALE) ADER discontinuous Galerkin (DG) methods on classic…
High order numerical discretizations of the Einstein-Euler equations in the Generalized Harmonic formulation
Stefano Muzzolon, Michael Dumbser, Olindo Zanotti +1
We propose two new alternative numerical schemes to solve the coupled Einstein-Euler equations in the Generalized Harmonic formulation. The first one is a finite difference (FD) Ce…
A structure-preserving semi-implicit finite volume scheme on vertex-staggered unstructured meshes
Elena Bernardelli, Elena Gaburro, Michael Dumbser
We present a novel structure-preserving semi-implicit finite volume method on vertex-based staggered meshes for the compatible discretization of first order systems of time-depende…
On general and complete multidimensional Riemann solvers for nonlinear systems of hyperbolic conservation laws
Elena Gaburro, Mario Ricchiuto, Michael Dumbser
In this work, we introduce a framework to design multidimensional Riemann solvers for nonlinear systems of hyperbolic conservation laws on general unstructured polygonal Voronoi-li…
High order well-balanced Arbitrary-Lagrangian-Eulerian ADER discontinuous Galerkin schemes on general polygonal moving meshes
Elena Gaburro
In this work, we present a novel family of high order accurate numerical schemes for the solution of hyperbolic partial differential equations (PDEs) which combines several geometr…
Discontinuous Galerkin schemes for hyperbolic systems in non-conservative variables: quasi-conservative formulation with subcell finite volume corrections
Elena Gaburro, Walter Boscheri, Simone Chiocchetti +1
We present a novel quasi-conservative arbitrary high order accurate ADER discontinuous Galerkin (DG) method allowing to efficiently use a non-conservative form of the considered pa…