High-order spectral element methods (SEM) for large-eddy simulation (LES) are still very
limited in industry. One of the main reasons behind this is the lack of robustness of SEM for …

We present hybridized discontinuous Galerkin (HDG) methods for ideal and resistive
compressible magnetohydrodynamics (MHD). The HDG methods are fully implicit, high …

We present the recent development of hybridizable and embedded discontinuous Galerkin
(DG) methods for wave propagation problems in fluids, solids, and electromagnetism. In …

In chaotic systems, such as turbulent flows, the solutions to tangent and adjoint equations
exhibit an unbounded growth in their norms. This behavior renders the instantaneous …

We present a unified framework for the hybridization of flux reconstruction (FR) schemes.
Specifically, we discuss the hybridized flux reconstruction (HFR) and interior-embedded flux …

We present a shock capturing method for large-eddy simulation of turbulent flows. The
proposed method relies on physical mechanisms to resolve and smooth sharp unresolved …

We present the hybridization of flux reconstruction methods for advection-diffusion problems.
Hybridization introduces a new variable into the problem so that it can be reduced via static …

View Video Presentation: https://doi. org/10.2514/6.2023-0853. vid This paper describes the
application of an implicit matrix-free discontinuous Galerkin method for hypersonic flow in …

We investigate the ability of discontinuous Galerkin (DG) methods to simulate under-
resolved turbulent flows in large-eddy simulation. The role of the Riemann solver and the …

In the spirit of making high-order discontinuous Galerkin (DG) methods more competitive,
researchers have developed the hybridized DG methods, a class of discontinuous Galerkin …