摘要
继实验流体力学和理论流体力学之后,计算流体力学作为一种以数值模拟为主要的研究方法,已经越来越受到人们的重视。随着计算机工业日新月异的发展,在过去的20余年中数值计算方法及其在计算流体力学中的应用也得到了飞速的进步,新的数值处理方法不断问世,原有的方法则得到进一步的充实与完善。在应用于传热与流动问题数值计算的众多方法中,基于有限体积法的SIMPLE算法,由于其概念简明、实施过程简单、数值特性优良而获得了特别广泛的应用,而先后出现SIMPLER、SIMPLEC、SIMPLEX等SIMPLE类算法,则使得算法的效率得到了相应的改善。
多重网格方法是促进代数方程迭代求解收敛速度的有效方法,在最近二十余年中,在流动与传热问题的数值计算中得到广泛的应用。然而将多重网格技术引入到SIMPLE类算法中,将SIMPLE类算法作为衰减误差分量的光顺器的问题却很少有学者研究。
本文的主要工作如下:
1.在同位网格系统下对SIMPLE类算法的性质进行研究。通过数值实验比较了该类方法在同位网格与交错网格中的计算结果。
2.将多重网格技术引入到SIMPLE类算法当中,从结果的分析可以看出,这一方法的引入不仅可以提高了算法的收敛速度,而且还节省了计算时间。经过比较可以看出,SIMPLEC用于多重网格的效果更佳。
3.为了适应复杂不规则的边界条件,利用适体坐标变换来克服天然河道复杂边界条件给模拟带来的困难,在同位网格系统中,将多重网格加速的SIMPLE类算法运用于宁夏黄河沙坡头某一弯段的二维水沙数学模型中,得出了比较好的结果。
Computational Fluid Dynamics(CFD)is more concerned in the research of Fluid Me-chanical. As important as the other two traditional research methods, experimental methodand theoretical methods.With the progress of computer technology, numerical method andits application in CFD have also obtained rapid progress in the past years.A number of nu-merical methods are created. Finite Volume Method (FVM)has clear concept, simple imple-mentation and good physical conservation property, so that it has obtained wide application.In FVM, SIMPLE is one of the most important algorithm. In order to improve the effi-ciency of algorithm, people proposed SIMPLER、SIMPLEC、SIMPLEX which are calledSIMPLE-family algorithms.
Multigrid approach is a good technique to improve the efficiency for solving algebraicequation. However only few scholars have applied multigrid method to SIMPLE-familyalgorithms.
The thesis is organized as following:
1.The research of SIMPLE-family algorithms on collocated grid system. Some nu-merical results comparing the methods on two kinds of staggered and collocated grid arepresented to illustrate the discussion.
2.Multigrid technique applied to the SIMPLE-family algorithms. By analysis,we cansee that this approach can accelerate considerably the convergence speed of SIMPLE-familyalgorithms. It is even better for the SIMPLE algorithm.
3.Multigrid method method is used to speed up the SIMPLE-family algorithms.Thisapproach is also used to the two-dimensional water-sediment numerical simulation of a bendof Yellow River in Ningxia Shapotou area. We get a relatively better results.
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