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 …

In this paper we will review a recent emerging paradigm shift in the construction and
analysis of high order Discontinuous Galerkin methods applied to approximate solutions of …

A generalized physics-based expression for the drag coefficient of spherical particles
moving in a fluid is developed. The proposed correlation incorporates essential rarefied …

We present a detailed description and verification of a discontinuous Galerkin finite element
method (DG) for the multi-component chemically reacting compressible Navier-Stokes …

We compare high-order methods including spectral difference (SD), flux reconstruction (FR),
the entropy-stable discontinuous Galerkin spectral element method (ES-DGSEM), modal …

In this paper, we develop a fully conservative, positivity-preserving, and entropy-bounded
discontinuous Galerkin scheme for simulating the multicomponent, chemically reacting …

High-order implicit shock tracking (fitting) is a new class of numerical methods to
approximate solutions of conservation laws with non-smooth features, eg, contact lines …

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 …

The moving discontinuous Galerkin finite element method with interface condition
enforcement is applied to the case of viscous flows. This method uses a weak formulation …

2. Hyper-reduction methods 2.1 Parametrized integrals 2.2 Empirical quadrature methods
2.3 Empirical interpolation methods 2.4 Integral interpolation methods 3. First-order …