Numerical Simulation of 2D Free-surface Potential Flows Using Modified Finite Point Method
Date Issued
2012
Date
2012
Author(s)
Tsu, I-Chen
Abstract
This study focuses on applicability of a numerical method in two problems, first, nonlinear liquid sloshing inside a two-dimensional tank that is subjected to horizontal forced oscillations, and second, a solitary wave propagating over a constant depth and over water with a gentle slope. The liquid flow is assumed to satisfy potential flow theory. In this study, a meshless numerical method which is named modified finite point method (MFPM) is employed. Based on collocation, this method uses polynomials as the local solution form needed in the collocation approach. The MFPM of Laplace equation is applied to solve the potential and velocity distributions at the grids of the computational domain and on the boundaries of the tank. An explicit time marching technique is developed by utilizing the leap-frog second-order central difference scheme. Lagrangian description are used to compute the position and the relative unknowns of the liquid particles on the free surface.
In the present study, the free surface displacements in a tank due to horizontally harmonic forced oscillation of two-dimensional rectangular tank are computed. It is shown that present numerical results agree very well with other research results (Lin & Liu, 2008). Present numerical model also demonstrated better computational efficiency.
For a solitary wave propagating over a water of constant depth, accuracy of present model is verified by observing no deformation and decay of the numerical wave form. When present model is applied to the case of a solitary wave over a water of a gentle slope, the shape of the wave steepens as it propagates over the slope and then turns over to break. The calculated wave shapes are compared with numerical results of Grilli and Subramanya (1996). Present model has demonstrated its capability in simulating a plunging solitary wave.
Subjects
Meshless method
Modified finite point method
Sloshing
Solitary wave
Potential flow
Plunging wave
Type
thesis
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