Structured mesh generation with smoothness controls

Abstract

SUMMARYIn geometrically complex domains, the Ryskin and Leal (RL) orthogonal mesh generation system may cause mesh distortion and overlapping problems when using the 'weak constraint' method with speciÿed boundary point distribution for all boundaries. To resolve these problems, an improved RL system with automatic smoothness control is proposed. In this improved RL system, the automatic smoothness control mechanism is based on ÿve types of smoothness conditions and includes the self-adjustment mechanism and the auto-evaluation mechanism for an empirical parameter. The proposed system is illustrated using several test examples. Several applications to natural domains are also demonstrated. It is shown that the improved RL system is capable of resolving the above problems at little cost of orthogonality.

Two‐dimensional adaptive mesh generation

“…Although there is little difference in mesh adaptivity between two methods, the current method produced much more orthogonal meshes. For current method, skewed meshes, which cause discontinuous transition of the mesh density distribution, exist in cases A1 and A2 due to the local strong orthogonal condition [13][14][15]. As for cases A3-A6, with consideration of mesh smoothness (s , s >0), both mesh smoothness and the transition have been significantly improved at little cost of mesh orthogonality.…”

“…In the RL system, they are equal to zero, while in Equation (19) they are formulated based on the orthogonal condition and the equal-distribution principle. An alternative simpler way to derive this equation is to directly substitute Equation (15) into Equation (10).…”

“…As pointed out in [13][14][15], the strong local orthogonal condition may cause serious mesh distortion and overlapping in geometrically complex domains, which eventually will affect mesh adaptivity. On the other hand, in regions of large gradients, the mesh may become increasingly distorted or skewed because of the equal-distribution principle (adaptivity), which may introduce new errors into the solution [16].…”

“…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.…”

Boundary treatment for 2D elliptic mesh generation in complex geometries

“…doi:10.1016/j.jcp.2008.05.008 constraints (specified boundary distribution) corresponding to the Dirichlet boundary conditions, if inappropriate nodal distribution is imposed along boundaries, the mesh quality cannot be guaranteed using the above systems. For examples, Ec ßa [2], and Zhang et al [11][12][13] pointed out that serious skewness or distortion and overlapping may occur using the RL system due to the local strong orthogonal conditions and, the conformal mapping may produce folded meshes due to the strong smoothness constraint-equal scale factors in all directions. According to the numerical tests of Ec ßa [2], favorable boundary nodal distribution can greatly improve mesh quality.…”