Related papers: Entropy and energy conservation for thermal atmosp…

We present a new hydrodynamic model for incompressible binary fluids that is thermodynamically consistent and non-isothermal. This model follows the generalized Onsager principle and Boussinesq approximation and preserves the volume of each…

The entropy conservative/stable algorithm of Friedrich~\etal (2018) for hyperbolic conservation laws on nonconforming p-refined/coarsened Cartesian grids, is extended to curvilinear grids for the compressible Euler equations. The primary…

Motivated by the notion that the mathematics of gravity can be reproduced from a statistical requirement of maximal entropy, we study the consequence of introducing an entropic source term in the Einstein-Hilbert action. For a spatially…

Internal energy, enthalpy and entropy are the key quantities to study thermodynamic properties of the moist atmosphere, because they correspond to the First (internal energy and enthalpy) and Second (entropy) Laws of thermodynamics. The aim…

This paper presents a thermodynamically consistent model for multicomponent electrolyte solutions. The first part of this paper derives the general governing equations for nonequilibrium systems within the theory of nonequilibrium…

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).…

In this paper, we investigate the asymptotic stability of finite-dimensional stochastic integrable Hamiltonian systems via information entropy. Specifically, we establish the asymptotic vanishing of Shannon entropy difference (with…

A mixed mimetic spectral element method is applied to solve the rotating shallow water equations. The mixed method uses the recently developed spectral element histopolation functions, which exactly satisfy the fundamental theorem of…

We present and test a general-purpose code, called PPASPH, for evolving self-gravitating fluids in astrophysics, both with and without a collisionless component. In PPASPH, hydrodynamical properties are computed by using the SPH (Smoothed…

By refining the method proposed in arXiv:2010.07660, entropy current and entropy density for a relativistic hydrostatic equilibrium system with spherical symmetry are constructed as a non-Noether conserved charge in the Einstein gravity…

Simulations of nano- to micro-meter scale fluidic systems under thermal gradients require consistent mesoscopic methods accounting for both hydrodynamic interactions and proper transport of energy. One such method is dissipative particle…

The approach to a substantiation of thermodynamics is offered. A conservative system of interacting elements, which is not in equilibrium, is used as a model. This system is then split into small subsystems that are accepted as being in…

We propose a finite element discretisation approach for the incompressible Euler equations which mimics their geometric structure and their variational derivation. In particular, we derive a finite element method that arises from a…

Radiation hydrodynamics simulations based on the one-fluid two-temperature model may violate the law of energy conservation because the governing equations are expressed in a nonconservative formulation. Here, we maintain the important…

Through an Hamiltonian action we write down the system of equations of motions for a mixture of thermocapillary fluids under the assumption that the internal energy is a function not only of the gradient of the densities but also of the…

This paper develops entropy stable (ES) adaptive moving mesh schemes for the 2D and 3D special relativistic hydrodynamic (RHD) equations. They are built on the ES finite volume approximation of the RHD equations in curvilinear coordinates,…

We show that a specific skew-symmetric form of nonlinear hyperbolic problems leads to energy and entropy bounds. Next, we exemplify by considering the compressible Euler equations in primitive variables, transform them to skew-symmetric…

We study mixed finite element methods for the rotating shallow water equations with linearized momentum terms but nonlinear drag. By means of an equivalent second-order formulation, we prove long-time stability of the system without energy…

We propose a mathematical formulation of the zeroth law of thermodynamics and develop a stochastic dynamical theory, with a consistent irreversible thermodynamics, for systems possessing sustained conservative stationary current in phase…

The metriplectic formalism is useful for describing complete dynamical systems which conserve energy and produce entropy. This creates challenges for model reduction, as the elimination of high-frequency information will generally not…