As computational astrophysics comes under pressure to become a precision science, there
is an increasing need to move to high accuracy schemes for computational astrophysics …

In this paper, a new type of high-order finite difference and finite volume multi-resolution
weighted essentially non-oscillatory (WENO) schemes is presented for solving hyperbolic …

In this paper we propose a novel arbitrary high order accurate semi-implicit space–time
discontinuous Galerkin method for the solution of the three-dimensional incompressible …

In this paper, central discontinuous Galerkin methods are developed for solving ideal
magnetohydrodynamic (MHD) equations. The methods are based on the original central …

In this article we propose a new family of high order staggered semi-implicit discontinuous
Galerkin (DG) methods for the simulation of natural convection problems. Assuming small …

In this work we present a mimetic spectral element discretization for the 2D incompressible
Navier–Stokes equations that in the limit of vanishing dissipation exactly preserves mass …

In the numerical simulation of ideal magnetohydrodynamics (MHD), keeping the pressure
and density always positive is essential for both physical considerations and numerical …

A spatially arbitrary high order, semi-implicit spectral discontinuous Galerkin (DG) scheme
for the numerical solution of the shallow water equations on staggered control volumes is …

Ideal magnetohydrodynamic (MHD) equations consist of a set of nonlinear hyperbolic
conservation laws, with a divergence-free constraint on the magnetic field. Neglecting this …

A well-balanced, spatially arbitrary high order accurate semi-implicit discontinuous Galerkin
scheme is presented for the numerical solution of the two dimensional shallow water …