Submitted to: International Journal for Numerical Methods in Fluids
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 11/7/2005
Publication Date: 1/4/2006
Citation: Zhang, Y., Jia, Y., Wang, S.S. 2006. Structured mesh generation with smoothness controls. International Journal for Numerical Methods in Fluids. Vol. 51: pp. 1255-1276.
Interpretive Summary: To resolve mesh distortion and overlapping problems in geometrically complex domains when using the Ryskin and Leal (RL) system with the “weak constraint” method, an improved RL system with automatic smoothness control is presented in this paper. The proposed method further improves the modified RL system with contribution factors proposed by Zhang et al. (2004), in which an empirical adjustable parameter alfa is used to control the strength of the contribution factors. The improved RL system directly controls the distortion function f using contribution factors to improve the overall mesh smoothness. Compared to the method proposed by Zhang et al. (2004), the present method does not need to calibrate the parameter to obtain good results. Instead, an automatic smoothness control mechanism, consisting of a self-adjustment mechanism and an auto-evaluation mechanism for alpha has been established based on five types of local smoothness: the local relative smoothness conditions in both the xi and eta directions, the local absolute smoothness conditions in xi and eta directions, and the local absolute smoothness conditions. An Averaged Deviation from the local Smoothness conditions (ADS) is used to comprehensively characterize the local mesh smoothness. The auto-evaluation mechanism is consistent with the self-adjustment mechanism and controlled by the maximum ADS. In order to avoid the inconsistency created by the spatially varied alpha, the constant value of alpha in the whole domain is used instead. The parameter alpha is dynamically adjusted during the iteration process. Although this technique is proposed for 2D structured mesh generation, the present method can be extended to 3D mesh generation as well. Examples and applications have shown that the proposed RL system is capable of generating nearly orthogonal meshes with a good balance in orthogonality and smoothness.
Technical Abstract: In geometrically complex domains, the RL (Ryskin and Leal) orthogonal mesh generation system may cause mesh distortion and overlapping problems when using the “weak constraint” method with specified 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 five 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.