263 citations · 631 across the 29 of their papers we have counts for
9 papers · 2 filters
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…
Curl constraint-preserving reconstruction and the guidance it gives for mimetic scheme design
Dinshaw S. Balsara, Roger Käppeli, Walter Boscheri +1
Several important PDE systems, like magnetohydrodynamics and computational electrodynamics, are known to support involutions where the divergence of a vector field evolves in diver…
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…