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边界元方法(BEM)是近代计算力学中的一种高效数值方法。由于采用相应的边界积分方程,使处理的问题减少了一维,从而给出的方程组就小得多,要求输入的数据也就大大地减少了,而所得结果的精度却高于有限元法。因此边界元法对于所谓的“区域法”,例如有限差分法(FDM)和有限元法(FEM)具有很强的竞争能力。 大量应用表明:边界元法与有限元法相比,不仅经济、易于使用,而且在许多工程领域,包括某些海洋参数的数值分析和预报方面都是很有发展前途的。 本文首先介绍了边界元方法的基本思想、数学原理和实施步骤,然后分别说明如何将这种方法用于更复杂的、非线性的、依时的问题。最后将讨论边界元法在一般粘性流体流动中的应用。
Boundary Element Method (BEM) is an efficient numerical method in modern computational mechanics. Due to the adoption of the corresponding boundary integral equation, the problem of processing is reduced by one dimension, so that the given system of equations is much smaller and the input data is greatly reduced. The accuracy of the obtained result is higher than the finite element method . The BEM is therefore highly competitive with the so-called “area laws,” such as the finite difference method (FDM) and the finite element method (FEM). The large number of applications shows that the boundary element method is not only economical and easy to use, but also promising for numerical analysis and forecasting of many engineering fields, including some marine parameters, compared with the finite element method. This paper first introduces the basic idea, mathematical principle and implementation steps of the BEM, then explains how to apply this method to the more complex, nonlinear and time-dependent problems respectively. Finally, the application of the boundary element method in general viscous fluid flow will be discussed.