Stabilized seventh-order dissipative compact scheme using simultaneous approximation terms  

作　　者：Jiaxian QIN Yaming CHEN Xiaogang DENG 

机构地区：[1]College of Aerospace Science and Engineering, National University of Defense Technology

出　　处：《Applied Mathematics and Mechanics(English Edition)》2019年第6期823-836,共14页应用数学和力学（英文版）

基　　金：supported by the National Natural Science Foundation of China(No.11601517);the Basic Research Foundation of National University of Defense Technology(No.ZDYYJ-CYJ20140101)

摘　　要：To ensure time stability of a seventh-order dissipative compact finite difference scheme, fourth-order boundary closures are used near domain boundaries previously. However, this would reduce the global convergence rate to fifth-order only. In this paper, we elevate the boundary closures to sixth-order to achieve seventh-order global accuracy. To keep the improved scheme time stable, the simultaneous approximation terms (SATs) are used to impose boundary conditions weakly. Eigenvalue analysis shows that the improved scheme is time stable. Numerical experiments for linear advection equations and one-dimensional Euler equations are implemented to validate the new scheme.To ensure time stability of a seventh-order dissipative compact finite difference scheme, fourth-order boundary closures are used near domain boundaries previously.However, this would reduce the global convergence rate to fifth-order only. In this paper,we elevate the boundary closures to sixth-order to achieve seventh-order global accuracy.To keep the improved scheme time stable, the simultaneous approximation terms(SATs)are used to impose boundary conditions weakly. Eigenvalue analysis shows that the improved scheme is time stable. Numerical experiments for linear advection equations and one-dimensional Euler equations are implemented to validate the new scheme.

关 键 词：HIGH-ORDER SCHEME compact SCHEME time stability simultaneous approximation TERM (SAT) 

分 类 号：O241[理学—计算数学]