基于MFS无网格方法的船舶耐波性预报

文章提出了一种新的基于MFS法(Method of Fundamental Solutions,即基本解法)的求解船舶势流问题的无网格数值方法。该方法采用势流控制方程的基本解表达流场中的速度势,可以得到任意阶连续的速度势导数;另外,通过引入流场虚边界的概念避免了传统边界元方法中存在奇点的问题。相比传统的边界元方法,MFS法具有无奇性、不依赖网格、不涉及数值积分、数学原理简单和算法易于编程实现的优势。文中对于MFS法在求解浅水二维剖面水动力系数中的应用进行了探索,提出了一套实用的数值算法,并进一步结合频域切片法计算了Wigley船体的垂荡和纵摇响应,通过和频域面元法及试验结果的对比验证了方法的正确性和实用性;最后应用开发的程序分析了不同水深和航速对于耐波性的影响。该研究开创性地将MFS方法应用到了船舶水动力研究领域,为之后更深入广泛地应用这一特性优良的数值方法提供了有益的参考。

Ship seakeeping prediction based on MFS meshfree scheme

This paper presents a novel meshfree numerical scheme based on MFS (Method of Fundamental Solutions) for solving ship potential flow problems. This method adopts the fundamental solution of the po-tential flow control equation to represent the velocity potentials and can obtain any degree of continous ve-locity potential derivative. Moreover, through the introduction of pseudo boundary, the singularity in con-ventional Boundary Element Method (BEM) is circumvented. Compared with BEM, MFS has the merits of being desingularized, meshfree, integration-free, mathematically simple and easy for programming. This study explores the application of MFS in computing the hydrodynamic coefficients of two dimensional sec-tion in water of finite depth and proposes a practical numerical scheme; furthermore, MFS is combined with frequency domain strip theory to predict the heave and pitch response of a Wigley hull. The validity of the proposed numerical scheme is proved through comparison with panel method and experimental result. Final-ly, the influence of water depth and forward speed on seakeeping is studied using the current scheme. This study innovatively applies MFS into the filed of ship hydrodynamics and can provide some guidance for the future development of MFS.