263 citations · 433 across the 8 of their papers we have counts for
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A posteriori subcell finite volume limiter for general PNPM schemes: applications from gasdynamics to relativistic magnetohydrodynamics
Elena Gaburro, Michael Dumbser
In this work, we consider the general family of the so called ADER PNPM schemes for the numerical solution of hyperbolic partial differential equations with \textit{arbitrary} high…
High order ADER-DG schemes for the simulation of linear seismic waves induced by nonlinear dispersive free-surface water waves
Caterina Bassi, Saray Busto, Michael Dumbser
In this paper, we propose a unified and high order accurate fully-discrete one-step ADER Discontinuous Galerkin method for the simulation of linear seismic waves in the sea bottom…
A hyperbolic reformulation of the Serre-Green-Naghdi model for general bottom topographies
Caterina Bassi, Luca Bonaventura, Saray Busto Ulloa +1
We present a novel hyperbolic reformulation of the Serre-Green-Naghdi (SGN) model for the description of dispersive water waves. Contrarily to the classical Boussinesq-type models,…
A novel staggered semi-implicit space-time discontinuous Galerkin method for the incompressible Navier-Stokes equations
Francesco Lohengrin Romeo, Michael Dumbser, Maurizio Tavelli
A new high order accurate staggered semi-implicit space-time discontinuous Galerkin (DG) method is presented for the simulation of viscous incompressible flows on unstructured tria…
On numerical methods for hyperbolic PDE with curl involutions
Michael Dumbser, Simone Chiocchetti, Ilya Peshkov
In this paper we present three different numerical approaches to account for curl-type involution constraints in hyperbolic partial differential equations for continuum physics. Al…
Space-time adaptive ADER discontinuous Galerkin schemes for nonlinear hyperelasticity with material failure
Maurizio Tavelli, Simone Chiocchetti, Evgeniy Romenski +2
We are concerned with the numerical solution of a unified first order hyperbolic formulation of continuum mechanics that originates from the work of Godunov, Peshkov and Romenski (…