Related papers: Asymptotic-preserving deterministic particle metho…
We develop an asymptotic-preserving scheme to solve evolution problems containing stiff transport terms. This scheme is based to a micro-macro decomposition of the unknown, coupled with a stabilization procedure. The numerical method is…
In this paper, we develop and implement an efficient asymptotic-preserving (AP) scheme to solve the gas mixture of Boltzmann equations under the disparate mass scaling relevant to the so-called "epochal relaxation" phenomenon. The disparity…
Asymptotic preserving (AP) schemes are targeting to simulate both continuum and rarefied flows. Many AP schemes have been developed and are capable of capturing the Euler limit in the continuum regime. However, to get accurate Navier-Stokes…
We propose a novel deterministic particle method to numerically approximate the Landau equation for plasmas. Based on a new variational formulation in terms of gradient flows of the Landau equation, we regularize the collision operator to…
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 propose a novel score-based particle method for solving the Landau equation in plasmas, that seamlessly integrates learning with structure-preserving particle methods [arXiv:1910.03080]. Building upon the Lagrangian viewpoint of the…
We perform the asymptotic analysis of parabolic equations with stiff transport terms. This kind of problem occurs, for example, in collisional gyrokinetic theory for tokamak plasmas, where the velocity diffusion of the collision mechanism…
In this paper, we first extend the micro-macro decomposition method for multiscale kinetic equations from the BGK model to general collisional kinetic equations, including the Boltzmann and the Fokker-Planck Landau equations. The main idea…
In this paper, a new asymptotic preserving (AP) scheme is proposed for the anisotropic elliptic equations. Different from previous AP schemes, the actual one is based on first-order system least-squares for second-order partial differential…
Radiation transport problems are posed in a high-dimensional phase space, limiting the use of finely resolved numerical simulations. An emerging tool to efficiently reduce computational costs and memory footprint in such settings is…
In this paper, we will develop a class of high order asymptotic preserving (AP) discontinuous Galerkin (DG) methods for nonlinear time-dependent gray radiative transfer equations (GRTEs). Inspired by the work \cite{Peng2020stability}, in…
We design a variational asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck system with the high field scaling, which describes the Brownian motion of a large system of particles in a surrounding bath. Our scheme builds on an…
We propose a two-dimensional asymptotic preserving scheme for linear transport equations with diffusive scalings. It is an extension of the time splitting developed by Jin, Pareschi and Toscani [SINUM,2000], but uses spatial discretizations…
In this paper, we propose a general framework to design asymptotic preserving schemes for the Boltzmann kinetic kinetic and related equations. Numerically solving these equations are challenging due to the nonlinear stiff collision (source)…
A three species one-dimensional kinetic model is presented for a spatially homogeneous weakly ionized plasma subjected to the action of a time varying electric field. Planar geometry is assumed, which means that the plasma dynamics evolves…
We develop a mathematically rigorous framework for simulating \emph{multiscale physical systems} using quantum computational resources, by translating the \emph{language of asymptotic-preserving (AP) schemes} into the formalism of quantum…
The present paper is devoted to the convergence analysis of an asymptotic preserving particle scheme designed to serve as a particle pusher in a Particle-In-Cell (PIC) method for the Vlasov equation with a strong inhomogeneous magnetic…
We propose a new pressure-based structure-preserving (SP) and quasi asymptotic preserving (AP) staggered semi-implicit finite volume scheme for the unified first order hyperbolic formulation of continuum mechanics. The unified model is…
In this study, we investigate the Shallow Water Equations incorporating source terms accounting for Manning friction and a non-flat bottom topology. Our primary focus is on developing and validating numerical schemes that serve a dual…
We propose an asymptotic-preserving (AP), uniformly convergent numerical scheme for the relativistic collisional Drift-Kinetic Equation (rDKE) to simulate runaway electrons in axisymmetric toroidal magnetic field geometries typical of…