Related papers: Multi-Scale Kinetic Simulation: Asymptotic Preserv…

In this paper, some theoretical aspects will be addressed for the asymptotic preserving DG-IMEX schemes recently proposed in [J. Jang, F. Li, J.-M. Qiu and T. Xiong, submitted, arxiv:1306.0227] for kinetic transport equations under a…

We consider a linear kinetic transport equation under a diffusive scaling, that converges to a diffusion equation as the Knudsen number $\varepsilon\rightarrow0$. In [3, 21], to achieve the asymptotic preserving (AP) property and…

For linear transport and radiative heat transfer equations with random inputs, we develop new generalized polynomial chaos based Asymptotic-Preserving stochastic Galerkin schemes that allow efficient computation for the problems that…

In this paper, we develop high-order asymptotic preserving (AP) schemes for the BGK equation in a hyperbolic scaling, which leads to the macroscopic models such as the Euler and compressible Navier-Stokes equations in the asymptotic limit.…

In this paper, uniformly unconditionally stable first and second order finite difference schemes are developed for kinetic transport equations in the diffusive scaling. We first derive an approximate evolution equation for the macroscopic…

In this paper, we develop a family of high order asymptotic preserving schemes for some discrete-velocity kinetic equations under a diffusive scaling, that in the asymptotic limit lead to macroscopic models such as the heat equation, the…

In this paper, we propose a general framework for designing numerical schemes that have both well-balanced (WB) and asymptotic preserving (AP) properties, for various kinds of kinetic models. We are interested in two different parameter…

A class of high order asymptotic preserving (AP) schemes has been developed for the BGK equation in Xiong et. al. (2015) [37], which is based on the micro-macro formulation of the equation. The nodal discontinuous Galerkin (NDG) method with…

The unified gas kinetic scheme (UGKS) of K. Xu et al. [K. Xu and J.-C. Huang, J. Comput. Phys., 229, pp. 7747--7764, 2010], originally developed for multiscale gas dynamics problems, is applied in this paper to a linear kinetic model of…

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…

In this work we construct a high-order Asymptotic-Preserving (AP) Implicit-Explicit (IMEX) scheme for the ES-BGK model for gas mixtures introduced in [Brull, Commun. Math. Sci., 2015]. The time discretization is based on the IMEX strategy…

We present an asymptotic preserving scheme based on a micro-macro decomposition for stochastic linear transport equations in kinetic and diffusive regimes. We perfom a mathematical analysis and prove that the scheme is uniformly stable with…

The kinetic theory provides a physical basis for developing multiscal methods for gas flows covering a wide range of flow regimes. A particular challenge for kinetic schemes is whether they can capture the correct hydrodynamic behaviors of…

In this paper, we develop a stochastic Asymptotic-Preserving (sAP) scheme for the kinetic chemotaxis system with random inputs, which will converge to the modified Keller-Segel model with random inputs in the diffusive regime. Based on the…

We develop a novel multilevel asymptotic-preserving Monte Carlo method, called Multilevel Kinetic-Diffusion Monte Carlo (ML-KDMC), for simulating the kinetic Boltzmann transport equation with a Bhatnagar-Gross-Krook (BGK) collision…

In our recent work [22], a family of high order asymptotic preserving (AP) methods, termed as IMEX-LDG methods, are designed to solve some linear kinetic transport equations, including the one-group transport equation in slab geometry and…

In this work, high order asymptotic preserving schemes are constructed and analysed for kinetic equations under a diffusive scaling. The framework enables to consider different cases: the diffusion equation, the advection-diffusion equation…

We develop novel asymptotic-preserving (AP) deterministic particle methods for collisional plasma models, including both Landau--Fokker--Planck and Dougherty collision operators, under hydrodynamic scaling. Our schemes treat the non-stiff…

We propose a multilevel Monte Carlo method for a particle-based asymptotic-preserving scheme for kinetic equations. Kinetic equations model transport and collision of particles in a position-velocity phase-space. With a diffusive scaling,…

We present a positive and asymptotic preserving numerical scheme for solving linear kinetic, transport equations that relax to a diffusive equation in the limit of infinite scattering. The proposed scheme is developed using a standard…