Adaptive OrderWENO Reconstructions for the Semi-Lagrangian Finite Difference Scheme for Advection Problem  

作　　者：Jiajie Chen Xiaofeng Cai Jianxian Qiu Jing-Mei Qiu 

机构地区：[1]Department of Mathematical Sciences,University of Delaware,Newark,DE,19717,USA [2]School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing,Xiamen University,Xiamen,Fujian 361005,P.R.China

出　　处：《Communications in Computational Physics》2021年第6期67-96,共30页计算物理通讯（英文）

摘　　要：We present a new conservative semi-Lagrangian finite difference weighted essentially non-oscillatory scheme with adaptive order.This is an extension of the conservative semi-Lagrangian(SL)finite difference WENO scheme in[Qiu and Shu,JCP,230(4)(2011),pp.863-889],in which linear weights in SL WENO framework were shown to not exist for variable coefficient problems.Hence,the order of accuracy is not optimal from reconstruction stencils.In this paper,we incorporate a recent WENO adaptive order(AO)technique[Balsara et al.,JCP,326(2016),pp.780-804]to the SL WENO framework.The new scheme can achieve an optimal high order of accuracy,while maintaining the properties of mass conservation and non-oscillatory capture of solutions from the original SL WENO.The positivity-preserving limiter is further applied to ensure the positivity of solutions.Finally,the scheme is applied to high dimensional problems by a fourth-order dimensional splitting.We demonstrate the effectiveness of the new scheme by extensive numerical tests on linear advection equations,the Vlasov-Poisson system,the guiding center Vlasov model as well as the incompressible Euler equations.

关 键 词：SEMI-LAGRANGIAN weighted essentially nonoscillatory WENO adaptive order reconstruction finite difference mass conservation Vlasov-Poisson incompressible Euler 

分 类 号：O17[理学—数学]