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首页> 外文会议>FED-vol.260; ASME International Mechanical Engineering Congress and Exposition; 20041113-19; Anaheim,CA(US) >DEVELOPING AN EFFICIENT MULTIGRID STRATEGY FOR SOLVING INCOMPRESSIBLE FLOW
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DEVELOPING AN EFFICIENT MULTIGRID STRATEGY FOR SOLVING INCOMPRESSIBLE FLOW

机译：制定有效的多重网格策略以解决不可压缩的流量

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摘要

In this work, a multigrid acceleration technique is suitably developed for solving the two-dimensional incompressible Navier-Stokes equations using an implicit finite element volume method. In this regard, the solution domain is broken into a huge number of quadrilateral finite elements. The accurate numerical solution of a flow field can be achieved if very fine grid resolutions are utilized. Unfortunately, the standard implicit solvers need more computational time to solve larger size of algebraic set of equations which normally arise if fine grid distributions are used. Past experience has shown that the convergence of classical relaxation schemes perform an initial rapid decrease of residuals followed by a slower rate of decrease. This point indicates that a relaxation procedure is efficient for eliminating only the high frequency components of the residuals. This problem can be overcome using multigrid method, i.e., carrying out the relaxation procedure on a series of different grid sizes. There are different prolongation operators to establish a multigrid procedure. A new prolongation expression is suitably developed in this work. It needs constructing data during refining and coarsening stages which is fulfilled using suitable finite element interpolators. The extended formulations are finally used to test several different problems with available benchmark solutions. The results indicate that the current multigrid strategy effectively improves the bandit solver performance.
机译：在这项工作中，为隐式有限元体积法求解二维不可压缩的Navier-Stokes方程而开发了一种多网格加速技术。在这方面，解域被分解为大量的四边形有限元。如果使用非常精细的网格分辨率，则可以实现流场的精确数值解。不幸的是，标准的隐式求解器需要更多的计算时间来求解较大的代数方程组，如果使用精细的网格分布，这通常会出现。过去的经验表明，经典松弛方案的收敛会导致残差的初始快速减小，然后是较慢的减小速率。这一点表明，松弛过程对于仅消除残差的高频分量是有效的。可以使用多重网格方法来克服该问题，即对一系列不同的网格尺寸执行松弛过程。有多种延长操作员可以建立多重网格程序。在这项工作中适当地开发了新的延长表达。它需要在细化和粗化阶段构造数据，这可以通过使用合适的有限元插值器来实现。最终，扩展的公式用于使用可用的基准解决方案测试几个不同的问题。结果表明，当前的多网格策略有效地提高了土匪求解器的性能。

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