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 a general family of subcell limiting strategies to construct robust high-order
accurate nodal discontinuous Galerkin (DG) schemes. The main strategy is to construct …

We introduce a simple and general framework for the construction of thermodynamically
compatible schemes for the numerical solution of overdetermined hyperbolic PDE systems …

In this paper we present a new family of semidiscrete and fully discrete finite volume
schemes for overdetermined, hyperbolic, and thermodynamically compatible PDE systems …

In this paper we propose a new reformulation of the first order hyperbolic model for unsteady
turbulent shallow water flows recently proposed in Gavrilyuk et al.(J Comput Phys 366: 252 …

This study proposes a novel method for developing discretization-consistent closure
schemes for implicitly filtered large eddy simulation (LES). Here, the induced filter kernel …

In this paper we propose a novel thermodynamically compatible finite volume scheme for
the numerical solution of the equations of magnetohydrodynamics (MHD) in one and two …

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

One of the challenges when simulating astrophysical flows with self-gravity is to compute the
gravitational forces. In contrast to the hyperbolic hydrodynamic equations, the gravity field is …

In this paper, we present a pressure-based semi-implicit numerical scheme for a first order
hyperbolic formulation of compressible two-phase flow with surface tension and viscosity …