【作者】 华蕾娜；

【导师】 王元战；

【作者基本信息】 天津大学 ， 港口、海岸及近海工程， 2005， 硕士

【摘要】 与实验室的试验研究和现场的观测研究相比较,数值波浪水槽有着极为突出的优点。然而,如何处理好自由表面是建立数值波浪水槽的重点、难点之一,本文的主要工作为ALE分步有限元法研究及其在自由表面水波问题中的应用。本文首先将ALE运动学描述引入到不可压缩黏性流体的控制方程(连续方程和N-S方程)中来,ALE描述通过定义一网格速度而拥有了传统的Lagrange描述和Euler描述所没有的异常的灵活性,并且物理意义明确。以此为基础,利用有限差分法的Euler显示格式进行控制方程时间域的离散,而空间域按照分步的思想由标准的Galerkin有限元法来离散,则得到ALE描述下的分步有限元格式。此分步格式的压力Poisson方程由运动方程直接推导得出,不同于速度修正法,因而其自然条件和本质条件物理意义明确,适用范围更广,并且即使速度插值函数和压强插值函数采取相同阶次,此分步格式也能获得较高精度的解,避免了混合插值在算法结构、计算时间和效率等方面的缺陷。采用ALE描述,在每一时间步上都需要进行网格更新,本文采用了一种简单而有效的方法,减轻了计算工作量。另外,本文还初步探讨了有限元格式的稳定性、集中质量法和相容质量法的优缺点等。将上述ALE分步有限元格式应用于水波自由振荡、水波非线性振荡、孤立波在等水深长方形水池内传播、孤立波在变地形长方形水池内传播等自由表面水波问题。在水波自由振荡算例中,计算结果表明此计算格式可以较好地模拟自由表面运动情况。在水波非线性振荡算例中,考察了此计算格式对高度非线性问题的适用性。孤立波在等水深长方形水池内传播的算例中,在相同的计算条件下,通过与文献[8]得到的计算结果比较,充分地说明了此计算格式可以以较高的精度模拟孤立波在水池内传播的运动情况,同时也表明了ALE描述方式与Lagrange描述方式相比在处理大变形水波问题方面的优势。孤立波在变地形长方形水池内传播的算例中,此计算格式成功地模拟了孤立波因受变地形的影响而发生的变形、传播过程,表明了对于那些比较复杂而难以应用解析方法进行分析的问题,此计算格式具有更强的适用性。更多还原

【Abstract】 Compared with experimental research and observational research, NumericalWave Tank (NWT) has the outstanding advantage. How to deal with the free surface,however, becomes one of the main difficulties of setting up a NWT. So, the main partof this thesis lays emphasis on ALE fractional-step finite element method andappliance of it to viscous free surface fluid flow problem.Firstly, employing ALE description derives the governing equations (continuityequation and N-S equation) in ALE form for unsteady, incompressible and viscousflow. ALE description has a very excellent flexibility that traditional pure Euleriandescription and pure Lagrangian description do not have, by utilizing a definition ofgrid velocity. Then, in order to obtain ALE fractional-step finite element method, thetime domain is discretized using Euler explicit scheme and according tofractional-step method, the space domain is dealed with by a Galerkin procedure inconjunction with the finite element approximation. Pressure Poisson equation isderived directly from the equation of motion, which is different from VelocityCorrection Method, so, the boundary conditions of the proposed method in the thesishave more specific physical meanings and more extensive applicability. Moreover,even if the interpolation functions of velocity and pressure have the same order, goodresults can be obtained, which avoids the disadvantages of mixed interpolation such asthe algorithm, computational time and computational efficiency. In ALE description,at every time step it is necessary to update the grids. This thesis advances a simple buteffective renew method to reduce the computational work. Additional, stability of thescheme is discussed simply;the advantages and disadvantages of Lumped MassMatrix and Consistent Mass Matrix are also studied.The viscous free surface flow problem is analysized by the proposed ALEfractional-step finite element method above, including free oscillation, nonlinearoscillation, propagation of a solitary wave in a rectangular channel with constantdepth and variable depth. In the first numerical case, the results show that this schemedoes a good job in pursuing the free surface position. The second numerical casepresents the applicability of this scheme to highly nonlinear problem. Through thethird numerical case, in the same computational conditions, the comparison with theresults from reference [8] demonstrates that this scheme is able to simulate accuratelythe motion of a solitary wave propagating in a rectangular channel with constant depth.It also gives a proof that ALE description overweighs Lagrangian description in termof solving large-deform problems. In the last numerical case, this scheme issuccessfully applied to the simulation of the propagation and deformation of a solitarywave due to the variable topography, which illustrates this scheme has more strongapplicability, especially for those complicated problems that can not be generallytreated by analytical method.更多还原