相关论文: A highly efficient asymptotic preserving IMEX meth…
This work is devoted to the numerical implementation of the quantum Bhatnagar- Gross-Krook (BGK) model for gas mixtures consisting of classical and quantum particles (fermions, bosons). We consider the model proposed by Bae, Klingenberg,…
We design a numerical scheme for transport equations with oscillatory periodic scattering coefficients. The scheme is asymptotic preserving in the diffusion limit as Knudsen number goes to zero. It also captures the homogenization limit as…
We consider the compressible Euler equations of gas dynamics with isentropic equation of state. Standard numerical schemes for the Euler equations suffer from stability and accuracy issues in the low Mach regime. These failures are…
In this paper, we develop an asymptotic-preserving and energy-conserving (APEC) Particle-In-Cell (PIC) algorithm for the Vlasov-Maxwell system. This algorithm not only guarantees that the asymptotic limiting of the discrete scheme is a…
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 these lectures three different methods of computing the asymptotic expansion of a Hermitian matrix integral is presented. The first one is a combinatorial method using Feynman diagrams. This leads us to the generating function of the…
In this paper, we present a conservative semi-Lagrangian finite-difference scheme for the BGK model. Classical semi-Lagrangian finite difference schemes, coupled with an L-stable treatment of the collision term, allow large time steps, for…
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 Gas-Kinetic Scheme (GKS), widely used in computational fluid dynamics for simulating hypersonic and other complicated flow phenomena, is extended in this work to electromagnetic problems by solving Maxwell's equations. In contrast to…
An asymptotic preserving and energy stable scheme for the barotropic Euler system under the low Mach number scaling is designed and analysed. A velocity shift proportional to the pressure gradient is introduced in the convective fluxes,…
Based on the Hermite expansion of the distribution function, we introduce a Galerkin spectral method for the spatially homogeneous Boltzmann equation with the realistic inverse-power-law models. A practical algorithm is proposed to evaluate…
In this paper, the design and analysis of high order accurate IMEX finite volume schemes for the compressible Euler-Poisson (EP) equations in the quasineutral limit is presented. As the quasineutral limit is singular for the governing…
The accuracy and effectiveness of Hermite spectral methods for the numerical discretization of partial differential equations on unbounded domains, are strongly affected by the amplitude of the Gaussian weight function employed to describe…
In this work, we design and analyze an asymptotic preserving (AP), semi-implicit finite volume scheme for the scaled compressible isentropic Euler system with a singular pressure law known as the congestion pressure law. The congestion…
This minicourse contains a description of recent results on the modelling of rarefied gases in weakly non equilibrium regimes, and the numerical methods used to approximate the resulting equations. Therefore this work focuses on BGK type…
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…
A new class of implicit-explicit (IMEX) methods combined with a p-adaptive mixed finite element formulation is proposed to simulate the diffusion of reacting species. Hierarchical polynomial functions are used to construct an…
This work aims to extend the residual distribution (RD) framework to stiff relaxation problems. The RD is a class of schemes which is used to solve hyperbolic system of partial differential equations. Up to our knowledge, it was used only…
In this paper, we present two novel Asymptotic-Preserving Neural Networks (APNNs) for tackling multiscale time-dependent kinetic problems, encompassing the linear transport equation and Bhatnagar-Gross-Krook (BGK) equation with diffusive…
Ideal gases can be modeled by the Boltzmann equation from statistical physics. Instead of trying to track the position and velocity of a large number of gas molecules, it is possible to describe the particles with a particle distribution…