相关论文: An efficient Asymptotic-Preserving scheme for the …

We develop efficient asymptotic-preserving time discretization schemes to solve the disparate mass kinetic system of a binary gas or plasma in the "relaxation time scale" relevant to the epochal relaxation phenomenon. Since the resulting…

The design and analysis of a unified asymptotic preserving (AP) and well-balanced scheme for the Euler Equations with gravitational and frictional source terms is presented in this paper. The asymptotic behaviour of the Euler system in the…

The concern of the present work is the introduction of a very efficient Asymptotic Preserving scheme for the resolution of highly anisotropic diffusion equations. The characteristic features of this scheme are the uniform convergence with…

In this paper, we study an asymptotic preserving (AP), energy stable and positivity preserving semi-implicit finite volume scheme for the Euler-Poisson-Boltzmann (EPB) system in the quasineutral limit. The key to energy stability is the…

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…

In this paper, we develop the Asymptotic-Preserving Neural Networks (APNNs) approach to study the forward and inverse problem for the semiconductor Boltzmann equation. The goal of the neural network is to resolve the computational…

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…

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…

The paper focuses on the development of numerical methods for the compressible Euler equations. It is well-known that if the Mach number is small, the system becomes stiff and hence explicit schemes suffer from severe time-step…

We construct numerical schemes to solve kinetic equations with anomalous diffusion scaling. When the equilibrium is heavy-tailed or when the collision frequency degenerates for small velocities, an appropriate scaling should be made and the…

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…

We present the asymptotic transitions from microscopic to macroscopic physics, their computational challenges and the Asymptotic-Preserving (AP) strategies to efficiently compute multiscale physical problems. Specifically, we will first…

In this article we introduce an asymptotic preserving scheme designed to compute the solution of a two dimensional elliptic equation presenting large anisotropies. We focus on an anisotropy aligned with one direction, the dominant part of…

We apply the concept of Asymptotic Preserving (AP) schemes to the linearized p-system and discretize the resulting elliptic equation using standard continuous Finite Elements instead of Finite Differences. The fully discrete method is…

We introduce and study a notion of Asymptotic Preserving schemes, related to convergence in distribution, for a class of slow-fast Stochastic Differential Equations. In some examples, crude schemes fail to capture the correct limiting…

We develop and study an asymptotic-preserving (AP) numerical scheme for a linear kinetic equation in a large deviation regime. After applying a Hopf-Cole transform to the distribution function, the system exhibits the behavior of rare…

The main purpose of the present paper is to study from a numerical analysis point of view some robust methods designed to cope with stiff (highly anisotropic) elliptic problems. The so-called asymptotic-preserving schemes studied in this…

In this contribution, we address the numerical solutions of high-order asymptotic equivalent partial differential equations with the results of a lattice Boltzmann scheme for an inhomogeneous advection problem in one spatial dimension. We…

This paper presents an asymptotic preserving (AP) implicit-explicit (IMEX) scheme for solving the quantum BGK equation using the Hermite spectral method. The distribution function is expanded in a series of Hermite polynomials, with the…

In this paper we develop high-order asymptotic-preserving methods for the spatially inhomogeneous quantum Boltzmann equation. We follow the work in Li and Pareschi, where asymptotic preserving exponential Runge-Kutta methods for the…