非线性自由表面波问题的差分解法

吕玉麟; 李宝元

非线性自由表面波问题的差分解法

大连工学院工程力学研究所

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出版历程
- 收稿日期: 1983-12-16
- 刊出日期: 1985-02-15

Finite Difference Method of Transient Nonlinear Free Surface Wave Problems

Research Institute of Engineering Mechanics, Dalian Institute of Technology, Dalian

摘要

摘要: 本文提出计算二维非定常位势流动的有限差分法,流动是因自由表面任意瞬间扰动所产生的.自由表面上同时满足动力和运动的非线性条件.本方法的基本特征是利用坐标变换将时间相关的物理计算域变换为固定域;建立迭代格式解Poisson方程以求速度势;通过快速富氏变换化为三对角型代数方程组计算未知量,因而大量节省计算机时.为解非定常自由表面波浪问题提供了一个有效的方法.引用了两个例题验证方法的可行性.

Abstract: A finite difference method is developed for computing the two-dimensional transient potential flow generated by an impulse on the free surface. Both the dynamic and kinematic free surface conditions are considered in nonlinear version, the primary features of the present paper include the use of special coordinates transformations so that the geometry of the flow field is transformed into a time-invariant region, presents an iteration process, by which the velocity potential is computed as the solution of a Poisson equation, the application of fast Fourier transform (FFT) technique results in a tri-diagonal system of equations which can be readily solved by the Thomas algorithm, the computing time is significantly reduced. Thus an efficient technique for handling the transient potential problems is well justified. The feasibility of the present method is verified by two examples involving different initial disturbances.

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参考文献(14)

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