High Order Conservative Finite Difference/Fourier Spectral Methods for Inviscid Surface Quasi-Geostrophic Flows

作     者：Nan Zhang Zhiping Mao Tao Xiong 

作者机构：School of Mathematical SciencesXiamen UniversityXiamenFujian361005P.R.China School of Mathematical SciencesFujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific ComputingXiamen UniversityXiamenFujian361005P.R.China 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2022年第32卷第10期

页      面：1474-1509页

核心收录：

学科分类：07[理学] 0701[理学-数学] 0702[理学-物理学] 070101[理学-基础数学] 

基　　金：partially supported by NSFC grant No.11971025,NSF grant of Fujian Province No.2019J06002 the Fundamental Research Funds for the Central Universities(20720210037) 

主　　题：Finite difference WENO Fourier spectral fractional Laplacian surface quasigeostrophic flow 

摘      要：In this paper,we develop an effective conservative high order finite difference scheme with a Fourier spectral method for solving the inviscid surface quasigeostrophic equations,which include a spectral fractional Laplacian determining the vorticity for the transport velocity of the potential *** fractional Laplacian is approximated by a Fourier-Galerkin spectral method,while the time evolution of the potential temperature is discretized by a high order conservative finite difference *** essentially non-oscillatory(WENO)reconstructions are also considered for *** to a low regularity of problems involving such a fractional Laplacian,especially in the critical or supercritical regime,directly applying the Fourier spectral method leads to a very oscillatory transport velocity associated with the gradient of the vorticity,*** smooth *** of using an artificial filter,we propose to reconstruct the velocity from the vorticity with central difference *** results are performed to demonstrate the good performance of our proposed approach.