Optimized Schwarz Waveform Relaxation method for the incompressible Stokes problem

Duc Quang Bui, C. Japhet, P. Omnes
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引用次数: 0

Abstract

We propose and analyse the optimized Schwarz waveform relaxation (OSWR) method for the unsteady incompressible Stokes equations. Well-posedness of the local subdomain problems with Robin boundary conditions is proved. Convergence of the velocity is shown through energy estimates; however, pressure converges only up to constant values in the subdomains, and an astute correction technique is proposed to recover these constants from the velocity. The convergence factor of the OSWR algorithm is obtained through a Fourier analysis, and allows to efficiently optimize the space-time Robin transmission conditions involved in the OSWR method. Then, numerical illustrations for the two-dimensional unsteady incompressible Stokes system are presented to illustrate the performance of the OSWR algorithm.
不可压缩斯托克斯问题的优化施瓦茨波形松弛法
我们提出并分析了针对非稳态不可压缩斯托克斯方程的优化施瓦茨波形松弛(OSWR)方法。我们证明了具有 Robin 边界条件的局部子域问题的良好求解性。通过能量估计显示了速度的收敛性;然而,压力只收敛到子域中的恒定值,并提出了一种精明的修正技术来从速度中恢复这些恒定值。通过傅立叶分析获得了 OSWR 算法的收敛因子,从而可以有效优化 OSWR 方法中涉及的时空罗宾传输条件。然后,给出了二维非稳态不可压缩斯托克斯系统的数值示例,以说明 OSWR 算法的性能。
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