2D Orthogonal Grid Generation of an Irregular Region Using Method of fundamental solutions
Date Issued
2012
Date
2012
Author(s)
Li-Yang, Hong
Abstract
The purpose of this study is to develop numerical method to generate two dimensional orthogonal grids in irregular regions for further computations of grid-based numerical models. This is because grid-based numerical methods have been fully developed and most numerical models in common uses are still coded with grid-based methods. Grid generation techniques to provide input information of orthogonal, boundary-fitted grids are essential.
Making use of the orthogonality of the Cauchy-Riemann conditions, grid generation of the forward and inverse transformations were formulated by solving Laplace equations. The numerical method in this study is a meshless numerical method, based on the Method of fundamental solutions, MFS. For collocation, this method uses 2-D fundamental solution of Laplace equation as the solution form needed in the collocation. The advantage of this approach is not only the values of the function values but also the values of its derivatives can be easily obtained. The meshless numerical method is easier to generate computational points especially in irregular regions for its flexibility in distribution of the base points.. When irregular domain consists with the corner with obtuse angle, a complex mapping technique is employed to convert the irregular geometry into a hyper-rectangle. It is shown that accuracy of orthogonality can be improved since the hyper-rectangle mapped to rectangular domain is performed on the basis of conformal mapping theorem.
There are six benchmark problems examined in this study, including a semi-annulus, an area bounded by two triangles, a full annulus, a four-pointed star, a flower-like irregular region, and the surrounding area of Taiwan. Correctness of present model is verified by checking the orthogonality of the generated results or comparing with exact solutions. In present model, except at the corner of singular points, the generated results are very accurate.
Subjects
grid generation
Cauchy-Riemann condition
Laplace equation
Meshless method
Method of fundamental solutions
Boundary-fitted orthogonal grids
Type
thesis
File(s)![Thumbnail Image]()
Loading...
Name
ntu-101-R99521309-1.pdf
Size
23.32 KB
Format
Adobe PDF
Checksum
(MD5):8f102badc225904918ffbce8e0dd94c0