We consider multiphysics applications from algorithmic and architectural perspectives,
where “algorithmic” includes both mathematical analysis and computational complexity, and …

In this work, we design an arbitrary high order accurate nodal discontinuous Galerkin
spectral element type method for the one dimensional shallow water equations. The novel …

We derive an implicit-explicit (IMEX) formalism for the three-dimensional (3D) Euler
equations that allow a unified representation of various nonhydrostatic flow regimes …

We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element
approximation for the non-linear two dimensional shallow water equations with non …

We present a novel staggered semi-implicit hybrid finite volume/finite element method for the
numerical solution of the shallow water equations at all Froude numbers on unstructured …

We present a new family of high order accurate fully discrete one-step Discontinuous
Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of …

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 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 …

The aim of this work is to design implicit and semi-implicit high-order well-balanced finite-
volume numerical methods for 1D systems of balance laws. The strategy introduced by two …

The resolutions of interests in atmospheric simulations require prohibitively large
computational resources. Adaptive mesh refinement (AMR) tries to mitigate this problem by …