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 …

There have been growing research interests in high-order discontinuous schemes over
recent years. With established theoretical basis and framework, more efforts have recently …

This study is concerned with predicting surface heat transfer in viscous hypersonic flows
using high-order discontinuous Galerkin (DG) methods. Currently, finite-volume (FV) …

The stable and accurate approximation of discontinuities such as shocks on a finite
computational mesh is a challenging task. Detection of shocks or strong discontinuities in …

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 …

This paper presents a shock capturing artificial viscosity scheme for the compact high-order
finite volume methods in terms of the variational reconstructions on unstructured grids. The …

This paper develops an oscillation-free discontinuous Galerkin (OFDG) method for solving
the multi-component chemically reacting flows. Two common governing equations are …

We present an optimal transport approach for mesh adaptivity and shock capturing of
compressible flows. Shock capturing is based on a viscosity regularization of the governing …

We extend the monolithic convex limiting (MCL) methodology to nodal discontinuous
Galerkin spectral-element methods (DGSEMS). The use of Legendre-Gauss-Lobatto (LGL) …

When simulating hyperbolic conservation laws with discontinuous solutions, high-order
linear numerical schemes often produce undesirable spurious oscillations. In this paper, we …