Discontinuous Galerkin methods for hypersonic flows

DS Hoskin, RL Van Heyningen, NC Nguyen… - Progress in Aerospace …, 2024 - Elsevier
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 …

Facilitating the adoption of unstructured high-order methods amongst a wider community of fluid dynamicists

PE Vincent, A Jameson - Mathematical Modelling of Natural …, 2011 - cambridge.org
Theoretical studies and numerical experiments suggest that unstructured high-order
methods can provide solutions to otherwise intractable fluid flow problems within complex …

Isogeometric divergence-conforming B-splines for the steady Navier–Stokes equations

JA Evans, TJR Hughes - … Models and Methods in Applied Sciences, 2013 - World Scientific
We develop divergence-conforming B-spline discretizations for the numerical solution of the
steady Navier–Stokes equations. These discretizations are motivated by the recent theory of …

Static condensation, hybridization, and the devising of the HDG methods

B Cockburn - Building bridges: connections and challenges in …, 2016 - Springer
In this paper, we review and refine the main ideas for devising the so-called hybridizable
discontinuous Galerkin (HDG) methods; we do that in the framework of steady-state diffusion …

Hybridizable discontinuous Galerkin methods for partial differential equations in continuum mechanics

NC Nguyen, J Peraire - Journal of Computational Physics, 2012 - Elsevier
We present hybridizable discontinuous Galerkin methods for solving steady and time-
dependent partial differential equations (PDEs) in continuum mechanics. The essential …

High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics

NC Nguyen, J Peraire, B Cockburn - Journal of Computational Physics, 2011 - Elsevier
We present a class of hybridizable discontinuous Galerkin (HDG) methods for the numerical
simulation of wave phenomena in acoustics and elastodynamics. The methods are fully …

A hybridizable discontinuous Galerkin method for the Navier–Stokes equations with pointwise divergence-free velocity field

S Rhebergen, GN Wells - Journal of Scientific Computing, 2018 - Springer
We introduce a hybridizable discontinuous Galerkin method for the incompressible Navier–
Stokes equations for which the approximate velocity field is pointwise divergence-free. The …

Hybridizable discontinuous Galerkin methods for the time-harmonic Maxwell's equations

NC Nguyen, J Peraire, B Cockburn - Journal of Computational Physics, 2011 - Elsevier
We present two hybridizable discontinuous Galerkin (HDG) methods for the numerical
solution of the time-harmonic Maxwell's equations. The first HDG method explicitly enforces …

Analysis of a hybridizable discontinuous Galerkin method for the steady-state incompressible Navier-Stokes equations

A Cesmelioglu, B Cockburn, W Qiu - Mathematics of Computation, 2017 - ams.org
We present the first a priori error analysis of the hybridizable discontinuous Galerkin method
for the approximation of the Navier-Stokes equations proposed in J. Comput. Phys. vol. 230 …

A hybridizable discontinuous Galerkin method for the compressible Euler and Navier-Stokes equations

J Peraire, N Nguyen, B Cockburn - 48th AIAA aerospace sciences …, 2010 - arc.aiaa.org
In this paper, we present a Hybridizable Discontinuous Galerkin (HDG) method for the
solution of the compressible Euler and Navier-Stokes equations. The method is devised by …