相关论文: Comparison of some Entropy Conservative Numerical …

Entropy-conserving numerical fluxes are a cornerstone of modern high-order entropy-dissipative discretizations of conservation laws. In addition to entropy conservation, other structural properties mimicking the continuous level such as…

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…

Entropy-conservative numerical flux functions can be used to construct high-order, entropy-stable discretizations of the Euler and Navier-Stokes equations. The purpose of this short communication is to present a novel family of such…

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…

For the first time, a general two-parameter family of entropy conservative numerical fluxes for the shallow water equations is developed and investigated. These are adapted to a varying bottom topography in a well-balanced way, i.e.…

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 =…

Entropy stable schemes can be constructed with a specific choice of the numerical flux function. First, an entropy conserving flux is constructed. Secondly, an entropy stable dissipation term is added to this flux to guarantee dissipation…

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…

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…

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…

This paper introduces a family of entropy-conserving finite-difference discretizations for the compressible flow equations. In addition to conserving the primary quantities of mass, momentum, and total energy, the methods also preserve…

We develop structure-preserving numerical methods for the compressible Euler equations, employing potential temperature as a prognostic variable. We construct three numerical fluxes designed to ensure the conservation of entropy and total…

In this work we analyze the entropic properties of the Euler equations when the system is closed with the assumption of a polytropic gas. In this case, the pressure solely depends upon the density of the fluid and the energy equation is not…

In this work a non-conservative balance law formulation is considered that encompasses the rotating, compressible Euler equations for dry atmospheric flows. We develop a semi-discretely entropy stable discontinuous Galerkin method on…

In this paper, we propose a novel development in the context of entropy stable finite-volume/finite-difference schemes. In the first part, we focus on the construction of high-order entropy conservative fluxes. Already in [LMR2002], the…

In this article, we propose high order discontinuous Galerkin entropy stable schemes for ten-moment Gaussian closure equations, which is based on the suitable quadrature rules (see [8]). The key components of the proposed method are the use…

We present a novel combination of numerical techniques to improve the efficiency, accuracy, and robustness of multi-component compressible flow simulations. At the core of our approach is an Entropy-Stable formulation that preserves kinetic…

This work concerns the numerical approximation of a multicomponent compressible Euler system for a fluid mixture in multiple space dimensions on unstructured meshes with a high-order discontinuous Galerkin spectral element method (DGSEM).…

We demonstrate that the shallow water moment equations satisfy an auxiliary entropy conservation law, where the entropy function corresponds to the total energy. Additionally, we show that the classical Newtonian slip friction and Manning…

Many entropy-conservative and entropy-stable (summarized as entropy-preserving) methods for hyperbolic conservation laws rely on Tadmor's theory for two-point entropy-preserving numerical fluxes and its higher-order extension via flux…