Numerical Simulation of 3D Nonlinear Flows around a Vertical Cylinder
Date Issued
2010
Date
2010
Author(s)
Chao, Po-Ying
Abstract
The objective of this study is aimed to numerically simulate nonlinear waves for uniform flows passing through a vertical cylinder by using the MFS method, one of the meshless methods. The method uses the fundamental solution of three-dimensional Laplace equation to solve the velocity potential and its gradient. With the Mixed Eulerian-Lagragian free surface conditions, the elevation can be interpolated by updating calculated positions by two-dimensional multi-quadratic function, particularly the interface between the free surface and the cylinder. A three-level central second-order difference method (leap-frog method) has been used for time discretization to develop an explicit marching computation scheme.
Assuming the fluid is inviscid and incompressible, this study also employs moving coordinate transformation to accelerate a vertical cylinder with its bed in a still water from the rest to a terminal velocity in a short time. Present numerical model can easily reduced into a linear case by ignoring the nonlinear terms in the dynamic free surface boundary condition. Present numerical results are compared with results of previous study of Sadathosseini et al. (2008) and Kawamura (2002). Numerical results of nonlinear waves generated are also compared with calculated linear cases in order to see the nonlinear effects. It is found that present results show a variation trend of free surface displacement around the cylinder similar to those of Sadathosseini et al. (2008). A new nondimensional parameter of the stagnation elevation at the front point of the cylinder encountered the uniform flows to justify present results are physically more reasonable. But in Kawamura (2002) cases, the difference between present calculations and previous results are quite different. It is believed that the difference may possibly due to the phase difference between present computation and previous ones.
Subjects
Meshless numerical method
Nonlinear water wave
Fundamental solution
Mixed Eulerian-Lagrangian boundary condition
multiquadric function
Cylindrical potential flow field
Type
thesis
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