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 …

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 …

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 …

For the general class of residual distribution (RD) schemes, including many finite element
(such as continuous/discontinuous Galerkin) and flux reconstruction methods, an approach …

This work reports on the performances of a fully-discrete hp-adaptive entropy stable
discontinuous collocated Galerkin method for the compressible Naiver–Stokes equations …

This paper proposes an unconditionally energy stable method for incompressible heat
conductive fluids under the phase–field framework. We combine the complicated system by …

Recently, an approach known as relaxation has been developed for preserving the correct
evolution of a functional in the numerical solution of initial-value problems, using Runge …

The second paper of this series presents two robust entropy stable shock-capturing methods
for discontinuous Galerkin spectral element (DGSEM) discretizations of the compressible …

In this paper, we present an entropy-stable (ES) discretization using a nodal discontinuous
Galerkin (DG) method for the ideal multi-ion magneto-hydrodynamics (MHD) equations. We …