A High-Order Semi-Lagrangian Finite Difference Method for Nonlinear Vlasov and BGK Models  

作　　者：Linjin Li Jingmei Qiu Giovanni Russo 

机构地区：[1]Department of Mathematical Sciences,University of Delaware,Newark,DE 19717,USA [2]Department of Mathematics and Computer Science,University of Catania,Catania,Italy

出　　处：《Communications on Applied Mathematics and Computation》2023年第1期170-198,共29页应用数学与计算数学学报（英文）

基　　金：Research of Linjin Li and Jingmei Qiu is supported by the NSF grant NSF-DMS-1818924;the Air Force Office of Scientific Computing FA9550-18-1-0257 and the University of Delaware;the Italian Ministry of Instruction,University and Research(MIUR)to support this research with funds coming from the PRIN Project 2017,No.2017KKJP4X and ITN-ETN Horizon 2020 Project,Project Reference 642768.

摘　　要：In this paper,we propose a new conservative high-order semi-Lagrangian finite difference(SLFD)method to solve linear advection equation and the nonlinear Vlasov and BGK models.The finite difference scheme has better computational flexibility by working with point values,especially when working with high-dimensional problems in an operator splitting setting.The reconstruction procedure in the proposed SLFD scheme is motivated from the SL finite volume scheme.In particular,we define a new sliding average function,whose cell averages agree with point values of the underlying function.By developing the SL finite volume scheme for the sliding average function,we derive the proposed SLFD scheme,which is high-order accurate,mass conservative and unconditionally stable for linear problems.The performance of the scheme is showcased by linear transport applications,as well as the nonlinear Vlasov-Poisson and BGK models.Furthermore,we apply the Fourier stability analysis to a fully discrete SLFD scheme coupled with diagonally implicit Runge-Kutta(DIRK)method when applied to a stiff two-velocity hyperbolic relaxation system.Numerical stability and asymptotic accuracy properties of DIRK methods are discussed in theoretical and computational aspects.

关 键 词：SEMI-LAGRANGIAN WENO Finite difference Vlasov-Poisson BGK equation Linear stability 

分 类 号：O17[理学—数学]