Parallel-in-Time Simulation of Two-Dimensional, Unsteady, Incompressible Laminar Flows
Parallel-in-Time Simulation of Two-Dimensional, Unsteady, Incompressible Laminar Flows
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DOI：
10.1080/10407790500459379
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发表时间：
2006-03
期刊：
影响因子：
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通讯作者：
J. D. M. Trindade;J. Pereira
中科院分区：
文献类型：
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作者：
J. D. M. Trindade;J. Pereira
目前的工作报告了时间并行算法在求解非定常不可压缩纳维-斯托克斯方程中的应用。时间并行算法允许将问题的时域分解为多个子域。该解决方案基于粗略和精细时间网格计算的迭代使用。计算从粗时间网格上沿时域的顺序解开始，然后是迭代过程。更精细的时间网格上的时间演化是并行计算的。该迭代过程为问题解决方案提供了连续的修正。在求解抛物线椭圆纳维斯托克斯方程和连续性方程时，以这种预测器-校正器方式使用两个时间网格可能会出现一些问题。其中，我们分析了处理器数量或时间子域以及收敛所需迭代次数的影响。此外，还提出了同时并行化空间和时间域的算法的扩展。尽管所提出的方法是针对大量处理器而设计的，但与单处理器计算相比，可以使用很少数量的处理器来实现显着的计算机时间节省。
The present work reports an application of a parallel-in-time algorithm to the solution of the unsteady incompressible Navier-Stokes equations. The parallel-in-time algorithm allows one to decompose the time domain of the problem into several subdomains. The solution is based on the iterative use of a coarse- and a finer-time-grid calculation. Calculation starts with a sequential solution along the time domain on the coarse time grid, and this is followed by the iterative procedure. The temporal evolution on the finer time grid is calculated in parallel. This iterative procedure provides successive corrections for the problem solution. When solving the parabolic-elliptic Navier-Stokes and continuity equations, some problems may emerge from the use of two temporal grids in this predictor-corrector fashion. Among them, we have analyzed the influence of the number of processors, or time subdomains, and the number of iterations required for convergence. In addition, an extension of the algorithm to parallelize simultaneously the space and time domains is presented. Although the proposed methodologies are designed for a massive number of processors, significant computer time saving, compared with a single-processor calculation, could be achieved with a very small number of processors.