Research On ALE Fractional-Step Finite Element Method And Appliance Of It To Viscous Free Surface Fluid Flow

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.