相关论文: A structure-preserving implicit exponential time d…

A pore network modeling (PNM) framework for the simulation of transport of charged species, such as ions, in porous media is presented. It includes the Nernst-Planck (NP) equations for each charged species in the electrolytic solution in…

Some hyperbolic systems are known to include implicit preservation of differential constraints: these are for example the time conservation of the curl or the divergence of a vector that appear as an implicit constraint. In this article, we…

In this paper, we design a novel class of arbitrarily high-order structure-preserving numerical schemes for the time-dependent Gross-Pitaevskii equation with angular momentum rotation in three dimensions. Based on the idea of the scalar…

In this report, we propose a divergence-free preserving mixed finite element method (FEM) for the system of nonlinear fourth-order thermally driven active fluid equations. By introducing two auxiliary variables, we lower the complexity of…

Efficient modeling of dispersive materials via time-domain simulations of the Maxwell equations relies on the technique of auxiliary differential equations. In this approach, a material's frequency-dependent permittivity is represented via…

Recently, there has been growing interest in using physics-informed neural networks (PINNs) to solve differential equations. However, the preservation of structure, such as energy and stability, in a suitable manner has yet to be…

Stable, accurate, divergence-free simulation of magnetized supersonic turbulence is a severe test of numerical MHD schemes and has been surprisingly difficult to achieve due to the range of flow conditions present. Here we present a new,…

We develop a numerical algorithm for computing the effective drift and diffusivity of the steady-state behavior of an overdamped particle driven by a periodic potential whose amplitude is modulated in time by multiplicative noise and forced…

We present a numerical method to solve the optimal transport problem with a quadratic cost when the source and target measures are periodic probability densities. This method is based on a numerical resolution of the corresponding…

The robust, scalable simulation of flowing electrochemical systems is increasingly important due to the synergy between intermittent renewable energy and electrochemical technologies such as energy storage and chemical manufacturing. The…

The computation of the radiative transfer equation is expensive mainly due to two stiff terms: the transport term and the collision operator. The stiffness in the former comes from the fact that particles (such as photons) travels at the…

Higher-order time integration methods that unconditionally preserve the positivity and linear invariants of the underlying differential equation system cannot belong to the class of general linear methods. This poses a major challenge for…

An asymptotic-preserving (AP) implicit-explicit PN numerical scheme is proposed for the gray model of the radiative transfer equation, where the first- and second-order numerical schemes are discussed for both the linear and nonlinear…

We have obtained an electromagnetic PIC (EM-PIC) algorithm based on time-space-extended particle in cell model. In this model particles are shaped objects extended over time and space around Lagrangian markers. Sources carried by these…

We present an Asymptotic-Preserving 'all-speed' scheme for the simulation of compressible flows valid at all Mach-numbers ranging from very small to order unity. The scheme is based on a semi-implicit discretization which treats the…

In this paper, we consider numerical approximations for solving the nonlinear magneto-hydrodynamical system, that couples the Navier-Stokes equations and Maxwell equations together. A challenging issue to solve this model numerically is…

Higher order finite volume schemes for magnetohydrodynamics (MHD) and relativistic magnetohydrodynamics (RMHD) are very valuable because they allow us to carry out astrophysical simulations with very high accuracy. However, astrophysical…

The energy dissipation law and the maximum bound principle are two critical physical properties of the Allen--Cahn equations. While many existing time-stepping methods are known to preserve the energy dissipation law, most apply to a…

In this work, we develop a novel numerical scheme to solve the classical Keller--Segel (KS) model which simultaneously preserves its intrinsic mathematical structure and achieves optimal accuracy. The model is reformulated into a gradient…

Computational modeling of charged species transport has enabled the analysis, design, and optimization of a diverse array of electrochemical and electrokinetic devices. These systems are represented by the Poisson-Nernst-Planck (PNP)…