High-Order Semi-Lagrangian WENO Schemes Based on Non-polynomial Space for the Vlasov Equation  

作　　者：Andrew Christlieb Matthew Link Hyoseon Yang Ruimeng Chang 

机构地区：[1]Department of Computational Mathematics,Science and Engineering,Michigan State University,East Lansing,MI 48824,USA [2]Department of Mathematical Sciences,Xi'an Jiaotong-Liverpool University,Suzhou 215123,Jiangsu,China

出　　处：《Communications on Applied Mathematics and Computation》2023年第1期116-142,共27页应用数学与计算数学学报（英文）

基　　金：AFOSR and NSF for their support of this work under grants FA9550-19-1-0281 and FA9550-17-1-0394 and NSF grant DMS 191218。

摘　　要：In this paper,we present a semi-Lagrangian(SL)method based on a non-polynomial function space for solving the Vlasov equation.We fnd that a non-polynomial function based scheme is suitable to the specifcs of the target problems.To address issues that arise in phase space models of plasma problems,we develop a weighted essentially non-oscillatory(WENO)scheme using trigonometric polynomials.In particular,the non-polynomial WENO method is able to achieve improved accuracy near sharp gradients or discontinuities.Moreover,to obtain a high-order of accuracy in not only space but also time,it is proposed to apply a high-order splitting scheme in time.We aim to introduce the entire SL algorithm with high-order splitting in time and high-order WENO reconstruction in space to solve the Vlasov-Poisson system.Some numerical experiments are presented to demonstrate robustness of the proposed method in having a high-order of convergence and in capturing non-smooth solutions.A key observation is that the method can capture phase structure that require twice the resolution with a polynomial based method.In 6D,this would represent a signifcant savings.

关 键 词：Semi-Lagrangian methods WENO schemes High-order splitting methods Non-polynomial basis Vlasov equation Vlasov-Poisson system 

分 类 号：O17[理学—数学]