Related papers: A Fast Semi-implicit Method for Anisotropic Diffus…
To determine the electron heat flux density on macroscopic scales, the most widely used approach is to solve a diffusion equation through a multi-group technique. This method is however restricted to transport induced by temperature…
An anisotropic random barrier model is presented, in which the transition probabilities in different directions have different probability density functions. At low temperatures, the anisotropic long--time diffusion coefficients, obtained…
In this work, we propose a nonlinear stabilization technique for scalar conservation laws with implicit time stepping. The method relies on an artificial diffusion method, based on a graph-Laplacian operator. It is nonlinear, since it…
We study a diffusion model of phase field type, which consists of a system of two partial differential equations involving as variables the thermal displacement, that is basically the time integration of temperature, and the order…
Consider the linear Boltzmann equation of radiative transfer in a half-space, with constant scattering coefficient $\sigma$. Assume that, on the boundary of the half-space, the radiation intensity satisfies the Lambert (i.e. diffuse)…
The ambipolar diffusion approximation is used to model partially ionised plasma dynamics in a single fluid setting. To correctly apply the commonly used version of ambipolar diffusion, a set of criteria should be satisfied including the…
Thermal conduction is an important energy transfer and damping mechanism in astrophysical flows. Fourier's law - the heat flux is proportional to the negative temperature gradient, leading to temperature diffusion - is a well-known…
Context: Thermal conductivity provides important contributions to the energy evolution of the upper solar atmosphere, behaving as a non-linear concentration-dependent diffusion equation. Recently, different methods have been offered as…
We study finite-temperature magnetization transport in a one-dimensional anisotropic Heisenberg model, focusing in particular on the gapped phase. Using numerical simulations by two different methods, a propagation of localized wavepackets…
The Active Flux (AF) method is a compact, high-order finite volume scheme that enhances flexibility by introducing point values at cell interfaces as additional degrees of freedom alongside cell averages. The method of lines is employed…
We describe an optical method to directly measure position-dependent thermal diffusivity of reflective single crystal samples across a broad range of temperatures for condensed matter physics research. Two laser beams are used, one as a…
Diffusion problems with anisotropic features arise in the various areas of science and engineering fields. As a Lagrangian mesh-less method, SPH has a special advantage in addressing the diffusion problems due to the the benefit of dealing…
We present a novel asymptotic-preserving semi-implicit finite element method for weakly compressible and incompressible flows based on compatible finite element spaces. The momentum is sought in an $H(\mathrm{div})$-conforming space,…
We construct a monotone continuous $Q^1$ finite element method on the uniform mesh for the anisotropic diffusion problem with a diagonally dominant diffusion coefficient matrix. The monotonicity implies the discrete maximum principle.…
The atmospheres of planets (including Earth) and the outer layers of stars have often been treated in radiative transfer as plane-parallel media, instead of spherical shells, which can lead to inaccuracy, e.g. limb darkening. We give an…
We study the long-time dynamics of the nonlinear processes modeled by diffusion-transport partial differential equations in non-divergence form with drifts. The solutions are subject to some inhomogeneous Dirichlet boundary condition.…
We introduce a novel explicit and stable numerical algorithm to solve the spatially discretized heat or diffusion equation. We compare the performance of the new method with analytical and numerical solutions. We show that the method is…
In this paper we want to propose practical numerical methods to solve a class of initial-boundary problem of time-space fractional convection-diffusion equations (TSFCDEs). To start with, an implicit difference method based on two-sided…
A moving mesh finite difference method based on the moving mesh partial differential equation is proposed for the numerical solution of the 2T model for multi-material, non-equilibrium radiation diffusion equations. The model involves…
This work is devoted to the study of the influence of temperature anisotropy and parallel heat flux on the stability of supersonic shear flow in collisionless plasmas. Within a fluid-based framework, we employ the 16-moment transport…