相关论文: An entropy admissible time splitting scheme for a …

We present a modified simulated annealing method with a dynamical choice of the cooling temperature. The latter is determined via a closed-loop control and is proven to yield exponential decay of the entropy of the particle system. The…

A reaction-diffusion problem with a Caputo time derivative is considered. An integral discretization scheme on a graded mesh along with a decomposition of the exact solution is proposed. The truncation error estimate of the discretization…

In this paper, we propose a new class of splitting methods to solve the stochastic Langevin equation, which can simultaneously preserve the ergodicity and exponential integrability of the original equation. The central idea is to extract a…

Numerical simulation of compressible fluid flows is performed using the Euler equations. They include the scalar advection equation for the density, the vector advection equation for the velocity and a given pressure dependence on the…

We study the entropy solution for a class of systems of nonlocal conservation laws in which the convective flux is convoluted with a kernel in both spatial and temporal variables. This formulation models the flux dependence on the solution…

High-order Hadamard-form entropy stable multidimensional summation-by-parts discretizations of the Euler and compressible Navier-Stokes equations are considerably more expensive than the standard divergence-form discretization. In search of…

We present a novel technique for imposing non-linear entropy conservative and entropy stable wall boundary conditions for the resistive magnetohydrodynamic equations in the presence of an adiabatic wall or a wall with a prescribed heat…

An implicit Euler finite-volume scheme for general cross-diffusion systems with volume-filling constraints is proposed and analyzed. The diffusion matrix may be nonsymmetric and not positive semidefinite, but the diffusion system is assumed…

We consider the non-isothermal flow of a compressible fluid through pipes. Starting from the full set of Euler equations, we propose a variational characterization of solutions that encodes the conservation of mass, energy, and entropy in 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…

This paper presents the construction of two numerical schemes for the solution of hyperbolic systems with relaxation source terms. The methods are built by considering the relaxation system as a whole, without separating the resolution of…

Motivated by recent progresses in nonequilibrium Fluctuation Relations, we present a generalized time reversal for stochastic master equation systems with discrete states that is defined as a splitting of the rate matrix into irreversible…

We propose a general strategy for enforcing multiple conservation laws and dissipation inequalities in the numerical solution of initial value problems. The key idea is to represent each conservation law or dissipation inequality by means…

We propose a finite volume scheme for a class of nonlinear parabolic equations endowed with non-homogeneous Dirichlet boundary conditions and which admit relative en-tropy functionals. For this kind of models including porous media…

This paper presents the notion of a variation entropy. This concept is an entropy framework for the gradient of the solution of a conservation law instead of on the solution itself. It appears that all semi-norms are admissible variation…

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…

Structure-preserving numerical schemes for a nonlinear parabolic fourth-order equation, modeling the electron transport in quantum semiconductors, with periodic boundary conditions are analyzed. First, a two-step backward differentiation…

We investigate the numerical approximation of (discontinuous) entropy solutions to nonlinear hyperbolic conservation laws posed on a Lorentzian manifold. Our main result establishes the convergence of monotone and first-order finite volume…

Partial differential equations (PDEs) describing thermodynamically isolated systems typically possess conserved quantities (like mass, momentum, and energy) and dissipated quantities (like entropy). Preserving these conservation and…

We consider the numerical approximation of a system of partial differential equations involving a nonlinear Schr\"odinger equation coupled with a hyperbolic conservation law. This system arises in models for the interaction of short and…