Localized Radial Basis Function Differential Quadrature Method for Two-Dimensional Free Surface Problems
Date Issued
2011
Date
2011
Author(s)
Huang, Yi-Heng
Abstract
In this study, a modified local radial basis function differential quadrature (LRBF-DQ) method is applied to solve the two-dimensional non-linear free surface problems. The LRBF-DQ method presented here has high order accuracy. This numerical scheme is a meshless approach, so that the better efficiency of calculation is obtained. It is discretized by a weighted linear sum of functional values at the points neighboring its desired knot so as to obtain the differential value of the desired point. The conventional DQ method is easier to subject to the ill-condition of the computed matrix and has a higher limit to the computing mesh. This method is more stable than the conventional numerical scheme when the approximate solution of the governing equation is solved by numerical simulation. In simulating the numerical value of the free surface, the error will become higher as the calculation time is longer in the case that the influence of the non-linear item is very high. Therefore, it is easy to result in wrong conclusions. A sloshing problem with a little influence on the non-linearity will be used for verification at first in this study. If the non-linearity has a little influence on the problem of the free surface, this problem can be considered as a pseudo-linear problem of the free surface. Therefore, the analytical solution can be used to compare its results so as to ensure the numerical model is correct. In addition, this numerical mode will be used to simulate the sloshing problems which are highly affected by some non-linear items. With the experiment of these numerical values, it proves that the numerical model is capable of accurately solving the problems of the free surface which is highly affected by the non-linear items.
Subjects
local radial basis function differential quadrature (LRBF-DQ) method
non-linear
free surface
numerical model
meshless
sloshing problems
Type
thesis
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