Stabilized seventh-order dissipative compact scheme using simultaneous approximation terms

doi:10.1007/s10483-019-2483-7

Abstract

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

2010 MSC Number:

76M20
93D20

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

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