Related papers: Finite-difference compatible entropy-conserving sc…
This paper presents a novel structure-preserving scheme for Euler equations, focusing on the numerical conservation of entropy and kinetic energy. Explicit flux functions engineered to conserve entropy are introduced within the…
We present in this paper a pressure correction scheme for the drift-flux model combining finite element and finite volume discretizations, which is shown to enjoy essential stability features of the continuous problem: the scheme is…
Centered numerical fluxes can be constructed for compressible Euler equations which preserve kinetic energy in the semi-discrete finite volume scheme. The essential feature is that the momentum flux should be of the form $f^m_\jph =…
Two-fluid plasma flow equations describe the flow of ions and electrons with different densities, velocities, and pressures. We consider the ideal plasma flow i.e. we ignore viscous, resistive, and collision effects. The resulting system of…
This paper proposes a hierarchy of numerical fluxes for the compressible flow equations which are kinetic-energy and pressure equilibrium preserving and asymptotically entropy conservative, i.e., they are able to arbitrarily reduce the…
This study proposes a novel spatial discretization procedure for the compressible Euler equations which guarantees entropy conservation at a discrete level when an arbitrary equation of state is assumed. The proposed method, based on a…
Structure-preserving finite-difference schemes for general nonlinear fourth-order parabolic equations on the one-dimensional torus are derived. Examples include the thin-film and the Derrida-Lebowitz-Speer-Spohn equations. The schemes…
We discuss structure-preserving numerical discretizations for repulsive and attractive Euler-Poisson equations that find applications in fluid-plasma and self-gravitation modeling. The scheme is fully discrete and structure preserving in…
This study proposes a novel spatial discretization procedure for the compressible Euler equations that guarantees entropy conservation at a discrete level for thermally perfect gases. The procedure is based on a locally conservative…
We present a convergence analysis of a finite volume (FV) scheme for the multicomponent compressible Euler system in the framework of dissipative weak (DW) solutions. DW solutions were introduced as a generalized solution framework in…
We present a novel asymptotic-preserving semi-implicit finite element method for weakly compressible and incompressible flows based on compatible finite element spaces. The momentum is sought in an $H(\mathrm{div})$-conforming space,…
In this article, we propose high-order finite-difference entropy stable schemes for the two-fluid relativistic plasma flow equations. This is achieved by exploiting the structure of the equations, which consists of three independent flux…
We show that finite element discretizations of incompressible flow problems can be designed to ensure preservation/dissipation of kinetic energy not only globally but also locally. In the context of equal-order (piecewise-linear)…
In this work, we design an entropy stable, finite volume approximation for the ideal magnetohydrodynamics (MHD) equations. The method is novel as we design an affordable analytical expression of the numerical interface flux function that…
Entropy stabilization of the compressible Euler system is achieved by adapting the averages that are applied to the density and internal energy variables. The approach achieves non-linear robustness despite the use of simplified symmetric…
A semi-implicit in time, entropy stable finite volume scheme for the compressible barotropic Euler system is designed and analyzed and its weak convergence to a dissipative measure-valued (DMV) solution [E. Feireisl et al., Dissipative…
Recently, relaxation methods have been developed to guarantee the preservation of a single global functional of the solution of an ordinary differential equation. Here, we generalize this approach to guarantee local entropy inequalities for…
In this work, Entropy-Stable (ES) schemes are formulated for the multicomponent compressible Euler equations. Entropy-conservative (EC) and ES fluxes are derived. Particular attention is paid to the limit case of zero partial densities…
Entropy conservation and stability of numerical methods in gas dynamics have received much interest. Entropy conservative numerical fluxes can be used as ingredients in two kinds of schemes: Firstly, as building blocks in the subcell flux…
High order schemes are known to be unstable in the presence of shock discontinuities or under-resolved solution features for nonlinear conservation laws. Entropy stable schemes address this instability by ensuring that physically relevant…