Stabilized seventh-order dissipative compact scheme using simultaneous approximation terms

doi:10.1007/s10483-019-2483-7

Applied Mathematics and Mechanics (English Edition) ›› 2019, Vol. 40 ›› Issue (6): 823-836.doi: https://doi.org/10.1007/s10483-019-2483-7

Stabilized seventh-order dissipative compact scheme using simultaneous approximation terms

Jiaxian QIN, Yaming CHEN, Xiaogang DENG

College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China

收稿日期:2018-07-14 修回日期:2018-09-10 出版日期:2019-06-01 发布日期:2019-06-01
通讯作者: Yaming CHEN E-mail:chenym-08@163.com
基金资助:
Project supported by the National Natural Science Foundation of China (No. 11601517) and the Basic Research Foundation of National University of Defense Technology (No. ZDYYJ-CYJ20140101)

Stabilized seventh-order dissipative compact scheme using simultaneous approximation terms

Jiaxian QIN, Yaming CHEN, Xiaogang DENG

College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China

Received:2018-07-14 Revised:2018-09-10 Online:2019-06-01 Published:2019-06-01
Contact: Yaming CHEN E-mail:chenym-08@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (No. 11601517) and the Basic Research Foundation of National University of Defense Technology (No. ZDYYJ-CYJ20140101)

摘要/Abstract

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.

关键词: Melnikov method, subharmonic bifurcation, hyper-subharmonic bifurcation, compact scheme, simultaneous approximation term (SAT), high-order scheme, time stability

Abstract: 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.

Key words: Melnikov method, subharmonic bifurcation, hyper-subharmonic bifurcation, simultaneous approximation term (SAT), compact scheme, time stability, high-order scheme

中图分类号:

76M20
93D20

Jiaxian QIN, Yaming CHEN, Xiaogang DENG. Stabilized seventh-order dissipative compact scheme using simultaneous approximation terms[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(6): 823-836.

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Stabilized seventh-order dissipative compact scheme using simultaneous approximation terms

Stabilized seventh-order dissipative compact scheme using simultaneous approximation terms

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