Iterative circle-inserting algorithm CST3D-OC of truly orthogonal curvilinear grid for coastal or river modelling

3rd International Conference on Water Resource and Environment

地球科学;生态环境科学

Kim, H.^1 ; Lee, S.^1 ; Lee, J.^1 ; Lim, H.-S.^2

Kookmin University, Seoul, Korea, Republic of^1

Korea Institute of Ocean Science and Technology, Ansan, Korea, Republic of^2

关键词: Algebraic method;    Boundary curves;    Curvilinear grids;    Degree of freedom;    Elliptic partial differential equation;    Geometric method;    Orthogonal grid;    River modelling;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/82/1/012006/pdf
DOI  :  10.1088/1755-1315/82/1/012006

学科分类：环境科学（综合）

来源: IOP

【 摘 要 】

A geometric method to generate orthogonal curvilinear grid is proposed here. Elliptic partial differential equations have frequently been solved to find orthogonal grid positions, but questions on orthogonality have remained so far. Algebraic methods have also been developed to improve orthogonality, but their applications have been limited to special situations. When two confronting boundary lines of the quadrilateral boundaries are straight, and their positions are known, and we assume that some degree of freedom exists on the other two confronting boundary curves under the condition that the each curve passes through a point, we can assign a set of latitudinal curves in the domain using polynomials. The curves are expected not to fold on their own. The grid positions along longitudinal curves are found by inserting circles between two neighbouring latitudinal curves one by one. If the two curves are straight, the new grid point above the grid point of interest can be found geometrically. This algorithm involves iterations because the curves are not straight lines. The present new algorithm is applied to a domain, and produced almost perfect orthogonality, and similar aspect ratio compared to an existing partial differential equation approach. The present algorithm also can express almost quadrant domain. The present algorithm seems useful for generation of orthogonal curvilinear grids along coasts or rivers. Some example grids are demonstrated.