2D nearly orthogonal mesh generation

Abstract

SUMMARYThe 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 ÿrst method, the original RL system is modiÿed 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 modiÿed 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 modiÿed 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.

Structured mesh generation with smoothness controls

“…The proposed method is the further improvement of the modiÿed RL system with contribution factors proposed by Zhang et al [17], in which an empirical adjustable parameter is used to control the strength of the contribution factors.…”

“…The ÿnal values of for domains C and D in the present method are quite close to the parameter used in Reference [17], in which it is constant in both space and iterations and was set to 0.2 and 0.6 for these two same domains, respectively. And the mesh qualities of these two domains using both methods are also very close.…”

Two‐dimensional adaptive mesh generation

“…Equation (19) is an elliptic adaptive mesh generation system derived from the RL system (Equation (1)) according to the orthogonal condition (orthogonality) described by Equation (6) and the cell area equal-distribution principle (adaptivity) defined by Equation (14). The only difference between this equation and the RL system lies in the source terms P and Q.…”

“…The determination of the distortion function f in this system has been the main concern of many researchers [13][14][15]. Unlike the TTM system proposed by Thompson et al [9] which has been extended to adaptive mesh generation [1,6,10], no literature has reported that the RL system can be used for adaptive mesh generation.…”

Alternative Methods for Generating Elliptic Grids in Finite Volume Applications

“…Therefore, modifications on the OGG have also been proposed to generate nearly orthogonal grids (Akcelik et al, 2001;Zhang et al, 2004, Zhang et. Al, 2006a, Zhang et.…”