In recent years, high-order discontinuous Galerkin (DG) methods have emerged as an
attractive approach for numerical simulations of compressible flows. This paper presents an …

Theoretical studies and numerical experiments suggest that unstructured high-order
methods can provide solutions to otherwise intractable fluid flow problems within complex …

The order of accuracy and error magnitude of node-and cell-centered schemes are
examined on representative unstructured meshes and flowfield solutions for computational …

This article presents a novel shock‐capturing technique for the discontinuous Galerkin (DG)
method. The technique is designed for compressible flow problems, which are usually …

We introduce an adaptive viscosity regularization approach for the numerical solution of
systems of nonlinear conservation laws with shock waves. The approach seeks to solve a …

A new method of obtaining third-order accuracy on unstructured grid flow solvers is
presented. The method involves a simple correction to a traditional linear Galerkin scheme …

In this work, we present a novel higher-order smooth artificial viscosity method for the
discontinuous Galerkin spectral element method and related high order methods. A neural …

This paper presents a shock capturing technique for a staggered grid discontinuous spectral
element method (DSEM), which adds localized and smooth artificial viscosity to systems of …

Gibbs oscillation can show up near flow regions with strong temperature gradients in the
numerical simulation of nonhydrostatic mesoscale atmospheric flows when using the high …

The present paper addresses the development and implementation of the first r-adaptive
mesh refinement (r-AMR) algorithm for a high-order Flux Reconstruction solver. The r …