Solving the relativistic magnetohydrodynamics equations with ADER discontinuous Galerkin methods, a posteriori subcell limiting and adaptive mesh refinement

A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws

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 hyperbolic conservation laws in multiple space dimensions that works well for arbitrary high order of accuracy in space and time and that does not destroy the natural subcell resolution properties of the DG method. High...

Refinement and Connectivity Algorithms for Adaptive Discontinuous Galerkin Methods

Adaptive multiscale methods are among the many effective techniques for the numerical solution of partial differential equations. Efficient grid management is an important task in these solvers. In this paper we focus on this problem for discontinuous Galerkin discretization methods in 2 and 3 spatial dimensions and present a data structure for handling adaptive grids of different cell types in...

Divergence-Free Adaptive Mesh Refinement for Magnetohydrodynamics

Relativistic MHD with Adaptive Mesh Refinement

This paper presents a new computer code to solve the general relativistic magnetohydrodynamics (GRMHD) equations using distributed parallel adaptive mesh refinement (AMR). The fluid equations are solved using a finite difference Convex ENO method (CENO) in 3 + 1 dimensions, and the AMR is Berger-Oliger. Hyperbolic divergence cleaning is used to control the ∇ · B = 0 constraint. We present resul...

A positivity-preserving semi-implicit discontinuous Galerkin scheme for solving extended magnetohydrodynamics equations

Article history: Received 26 February 2014 Received in revised form 20 August 2014 Accepted 26 August 2014 Available online 3 September 2014