On GLM curl cleaning for a first order reduction of the CCZ4 formulation of the Einstein field equations
In this paper we propose an extension of the generalized Lagrangian multiplier method
(GLM) of Munz et al.[52],[30], which was originally conceived for the numerical solution of the …
(GLM) of Munz et al.[52],[30], which was originally conceived for the numerical solution of the …
Continuous finite element subgrid basis functions for discontinuous Galerkin schemes on unstructured polygonal Voronoi meshes
We propose a new high order accurate nodal discontinuous Galerkin (DG) method for the
solution of nonlinear hyperbolic systems of partial differential equations (PDE) on …
solution of nonlinear hyperbolic systems of partial differential equations (PDE) on …
High order ADER schemes and GLM curl cleaning for a first order hyperbolic formulation of compressible flow with surface tension
In this work, we introduce two novel reformulations of the weakly hyperbolic model for two-
phase flow with surface tension, recently forwarded by Schmidmayer et al. In the model, the …
phase flow with surface tension, recently forwarded by Schmidmayer et al. In the model, the …
A structure-preserving finite volume scheme for a hyperbolic reformulation of the Navier–Stokes–Korteweg equations
F Dhaouadi, M Dumbser - Mathematics, 2023 - mdpi.com
In this paper, we present a new explicit second-order accurate structure-preserving finite
volume scheme for the first-order hyperbolic reformulation of the Navier–Stokes–Korteweg …
volume scheme for the first-order hyperbolic reformulation of the Navier–Stokes–Korteweg …
Higher order divergence-free and curl-free interpolation on MAC grids
Divergence-free vector fields and curl-free vector fields play an important role in many types
of problems, including the incompressible Navier-Stokes equations, Maxwell's equations …
of problems, including the incompressible Navier-Stokes equations, Maxwell's equations …
Efficient WENO-based prolongation strategies for divergence-preserving vector fields
Adaptive mesh refinement (AMR) is the art of solving PDEs on a mesh hierarchy with
increasing mesh refinement at each level of the hierarchy. Accurate treatment on AMR …
increasing mesh refinement at each level of the hierarchy. Accurate treatment on AMR …
Globally divergence-free DG scheme for ideal compressible MHD
The high-accuracy solution of the MHD equations is of great interest in various fields of
physics, mathematics, and engineering. Higher-order DG schemes offer low dissipation and …
physics, mathematics, and engineering. Higher-order DG schemes offer low dissipation and …
Curl constraint-preserving reconstruction and the guidance it gives for mimetic scheme design
Several important PDE systems, like magnetohydrodynamics and computational
electrodynamics, are known to support involutions where the divergence of a vector field …
electrodynamics, are known to support involutions where the divergence of a vector field …
An exactly curl-free finite-volume scheme for a hyperbolic compressible barotropic two-phase model
We present a new second order accurate structure-preserving finite volume scheme for the
solution of the compressible barotropic two-phase model of Romenski et. al in multiple …
solution of the compressible barotropic two-phase model of Romenski et. al in multiple …
Making a synthesis of FDTD and DGTD schemes for computational electromagnetics
DS Balsara, JJ Simpson - IEEE Journal on Multiscale and …, 2020 - ieeexplore.ieee.org
A novel class of discontinuous Galerkin time-domain (DGTD) schemes, invented by the first
author, are presented that are capable of globally preserving the constraints that are …
author, are presented that are capable of globally preserving the constraints that are …