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Numerical Simulation Potential Flow Equations With Finite Difference Method

Posted on:2015-11-11Degree:MasterType:Thesis
Country:ChinaCandidate:G ZengFull Text:PDF
GTID:2180330431978033Subject:Computational Mathematics
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This dissertation is devoted to simulate the numerical solutions of the potential flow equations in a two dimensional tank. In this dissertation, the numerical solutions of the wave elevation on free surface are investigated in a liquid sloshing tank. The solutions of the sloshing problem have always been a challenge in terms of the nonlinear phenomenon and analytical solutions. We develop a Crank-Nicolson implicit scheme finite difference method for the potential flow equations. Crank-Nicolson implicit scheme is applied to discrete potential flow equations and its boundary conditions. The coordinate transformations are introduced to map the time-dependent irregular physical domain to a time-independent fixed square calculation domain which is divided by staggered mesh system. The iterative algorithm is adopted to solve the variables of the velocity potential and the wave elevation on the free surface, and the algorithm is compiled with Fortran language. The major works of this paper include three parts as follows:(1) Firstly, the finite difference method is adopted to solve the numerical solution of the linear potential flow equations. We simulate the elevation on the free surface with the initial small amplitude wave under different amplitude and different wave number in a two dimensional tank. We analyze the error values of the wave elevation on the free surface between the numerical solutions and the analytic solutions.(2) Secondly, we investigate the finite difference numerical solver of the nonlinear potential flow equations. We simulate the elevation on the free surface in a two dimensional tank with free oscillation motions. The numerical elevation is compared with the second order approximate solutions. At the same time, we also investigate the elevation on the surface with horizontal excited motion, vertical excited motion, coupling excited motion of the horizontal and vertical directions.(3)Finally, From the incompressible Navier-Stokes equation with dissipative term, we derive the nonlinear potential flow equations in a inviscid and irrotational fluid tank. We calculate the wave elevation on free surface under different dissipation coefficient with free oscillation motions. At the same time, we also investigate the wave elevation on the surface with the horizontal excited motion, vertical excited motion and the coupling excited motion with different dissipation coefficients.
Keywords/Search Tags:Finite difference method, Potential flow equations, Staggered meshsystem, Iterative algorithm, Crank-Nicolson implicit scheme, Fortran language
PDF Full Text Request
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