356 citations · 3.6k across the 47 of their papers we have counts for
12 papers · 1 filter
An Arbitrary-Lagrangian-Eulerian solver for relativistic detonation waves
Sara Rinaldi, Olindo Zanotti, Michael Dumbser
In this paper we study the dynamics of relativistic detonation waves theoretically and numerically. The reaction is physically accounted for by an extra term in the definition of t…
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…
Variational derivation and compatible discretizations of the Maxwell-GLM system
Michael Dumbser, Alessia Lucca, Ilya Peshkov +1
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…
Space-time adaptive ADER-DG schemes for dissipative flows: compressible Navier-Stokes and resistive MHD equations
Francesco Fambri, Michael Dumbser, Olindo Zanotti
This paper presents an arbitrary h.o. accurate ADER DG method on space-time adaptive meshes (AMR) for the solution of two important families of non-linear time dependent PDE for co…
Efficient conservative ADER schemes based on WENO reconstruction and space-time predictor in primitive variables
Olindo Zanotti, Michael Dumbser
We present a new version of conservative ADER-WENO finite volume schemes, in which both the high order spatial reconstruction as well as the time evolution of the reconstruction po…
High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: viscous heat-conducting fluids and elastic solids
Michael Dumbser, Ilya Peshkov, Evgeniy Romenski +1
This paper is concerned with the numerical solution of the unified first order hyperbolic formulation of continuum mechanics recently proposed by Peshkov & Romenski, denoted as HPR…
Space-time adaptive ADER discontinuous Galerkin finite element schemes with a posteriori sub-cell finite volume limiting
Olindo Zanotti, Francesco Fambri, Michael Dumbser +1
In this paper we present a novel arbitrary high order accurate discontinuous Galerkin (DG) finite element method on space-time adaptive Cartesian meshes (AMR) for hyperbolic conser…
High Order Cell-Centered Lagrangian-Type Finite Volume Schemes with Time-Accurate Local Time Stepping on Unstructured Triangular Meshes
Walter Boscheri, Michael Dumbser, Olindo Zanotti
We present a novel cell-centered direct Arbitrary-Lagrangian-Eulerian (ALE) finite volume scheme on unstructured triangular meshes that is high order accurate in space and time and…
A Posteriori Subcell Limiting of the Discontinuous Galerkin Finite Element Method for Hyperbolic Conservation Laws
Michael Dumbser, Olindo Zanotti, Raphael Loubere +1
The purpose of this work is to propose a novel a posteriori finite volume subcell limiter technique for the Discontinuous Galerkin finite element method for nonlinear systems of hy…
High Order Space-Time Adaptive WENO Finite Volume Schemes for Non-Conservative Hyperbolic Systems
Michael Dumbser, Arturo Hidalgo, Olindo Zanotti
We present a class of high order finite volume schemes for the solution of non-conservative hyperbolic systems that combines the one-step ADER-WENO finite volume approach with spac…
ADER-WENO Finite Volume Schemes with Space-Time Adaptive Mesh Refinement
Michael Dumbser, Olindo Zanotti, Arturo Hidalgo +1
We present the first high order one-step ADER-WENO finite volume scheme with Adaptive Mesh Refinement (AMR) in multiple space dimensions. High order spatial accuracy is obtained th…
On Arbitrary-Lagrangian-Eulerian One-Step WENO Schemes for Stiff Hyperbolic Balance Laws
Michael Dumbser, Ariunaa Uuriintsetseg, Olindo Zanotti
In this article we present a new family of high order accurate Arbitrary Lagrangian-Eulerian one-step WENO finite volume schemes for the solution of stiff hyperbolic balance laws.…