2D nearly orthogonal mesh generation

摘要

The Ryskin and Leal (RL) system is the most widely used mesh generation system for the orthogonal mapping. However, when this system is used in domains with complex geometry, particularly in those with sharp corners and strong curvatures, serious distortion or overlapping of mesh lines may occur and an acceptable solution may not be possible. In the present study, two methods are proposed to generate nearly orthogonal meshes with the smoothness control. In the first method, the original RL system is modified by introducing smoothness control functions, which are formulated through the blending of the conformal mapping and the orthogonal mapping; while in the second method, the RL system is modified by introducing the contribution factors. A hybrid system of both methods is also developed. The proposed methods are illustrated by several test examples. Applications of these methods in a natural river channel are demonstrated. It is shown that the modified RL systems are capable of producing meshes with an adequate balance between the orthogonality and the smoothness for complex computational domains without mesh distortions and overlapping.