Related papers: Structure-preserving numerical calculation of wave…
In this paper, we propose stochastic structure-preserving schemes to compute the effective diffusivity for particles moving in random flows. We first introduce the motion of particles using the Lagrangian formulation, which is modeled by…
In this paper, we consider a system of one-dimensional parabolic PDEs, known as the KWC system, as a phase-field model for grain boundary motion. A key feature of this system is that the equation for the crystalline orientation angle is…
The classical numerical methods play important roles in solving wave equation, e.g. finite difference time domain method. However, their computational domain are limited to flat space and the time. This paper deals with the description of…
A new energy and enstrophy conserving scheme is evaluated using a suite of test cases over the global spherical domain or bounded domains. The evaluation is organized around a set of pre-defined properties: accuracy of individual opeartors,…
In this note we work on the construction of positive preserving numerical schemes for systems of stochastic differential equations. We use the semi discrete idea that we have proposed before proposing now a numerical scheme that preserves…
A conforming finite element scheme with mixed explicit-implicit time discretization for quasi-incompressible Navier-Stokes-Maxwell-Stefan systems in a bounded domain with periodic boundary conditions is presented. The system consists of the…
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…
In this paper, we present an energy-preserving exponentially integrable numerical method for stochastic wave equation with cubic nonlinearity and additive noise. We first apply the spectral Galerkin method to discretizing the original…
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 develop structure-preserving numerical methods for the Serre-Green-Naghdi equations, a model for weakly dispersive free-surface waves. We consider both the classical form, requiring the inversion of a non-linear elliptic operator, and a…
In this paper, we propose and analyze semi-implicit numerical schemes for the stochastic wave equation (SWE) with general nonlinearity and multiplicative noise. These numerical schemes, called stochastic scalar auxiliary variable (SAV)…
Finite difference schemes that preserve two conservation laws of a given partial differential equation can be found directly by a recently-developed symbolic approach. Until now, this has been used only for equations with quadratic…
We propose a new numerical approach to compute nonclassical solutions to hyperbolic conservation laws. The class of finite difference schemes presented here is fully conservative and keep nonclassical shock waves as sharp interfaces,…
We investigate discretization strategies for a recently introduced class of energy-based models. The model class encompasses classical port-Hamiltonian systems, generalized gradient flows, and certain systems with algebraic constraints. Our…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
Many differential equations with physical backgrounds are described as gradient systems, which are evolution equations driven by the gradient of some functionals, and such problems have energy conservation or dissipation properties. For…
We study the recently-proposed hyperbolic approximation of the Korteweg-de Vries equation (KdV). We show that this approximation, which we call KdVH, possesses a rich variety of solutions, including solitary wave solutions that approximate…
Symmetry- and conservation law-preserving finite difference discretizations are obtained for linear and nonlinear one-dimensional wave equations on five- and nine-point stencils, using the theory of Lie point symmetries of difference…
In this work we demonstrate that SVD-based model reduction techniques known for ordinary differential equations, such as the proper orthogonal decomposition, can be extended to stochastic differential equations in order to reduce the…
We consider the discretization and subsequent model reduction of a system of partial differential-algebraic equations describing the propagation of pressure waves in a pipeline network. Important properties like conservation of mass,…