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 …

We present Trixi. jl, a Julia package for adaptive high-order numerical simulations of
hyperbolic partial differential equations. Utilizing Julia's strengths, Trixi. jl is extensible, easy …

We develop error-control based time integration algorithms for compressible fluid dynamics
(CFD) applications and show that they are efficient and robust in both the accuracy-limited …

Effective relaxation methods are necessary for good multigrid convergence. For many
equations, standard Jacobi and Gauß–Seidel are inadequate, and more sophisticated …

Many modern discontinuous Galerkin (DG) methods for conservation laws make use of
summation by parts operators and flux differencing to achieve kinetic energy preservation or …

In computational fluid dynamics, the demand for increasingly multidisciplinary reliable
simulations, for both analysis and design optimization purposes, requires transformational …

Numerical simulation of shock-boundary layer interactions in the hypersonic regime has for
long been a challenge, plagued by high sensitivity of the surface predictions to grid and …

We present a new class of efficient and robust discontinuous spectral-element methods of
arbitrary order for nonlinear hyperbolic systems of conservation laws on curved triangular …

Industrially relevant computational fluid dynamics simulations frequently require vast
computational resources that are only available to governments, wealthy corporations, and …

We propose a parallel (distributed) version of the spectral proper orthogonal decomposition
(SPOD) technique. The parallel SPOD algorithm distributes the spatial dimension of the …