INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS Int. J. Numer. Meth. Fluids 2006; 51:1255–1276 Published online 4 January 2006 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/d.1150 Structured mesh generation with smoothness controls Yaoxin Zhang ∗; †; ‡ , Yafei Jia §; ¶ and Sam S. Y. Wang ‖; ∗∗ National Center for Computational Hydroscience and Engineering; The University of Mississippi; P.O. Box 1500; Oxford; MS 38677; U.S.A. SUMMARY In 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 specied 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 ve 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. Copyright ? 2006 John Wiley & Sons, Ltd. KEY WORDS: mesh generation; smoothness control; self-adjustment mechanism; auto-evaluation mechanism 1. INTRODUCTION Mesh generation is the art of mapping between the physical coordinates and the computational coordinates. Extensive researches (i.e. References [1–17]) in this area have been made. For a detailed review of researches and development in the 1990s, please refer to Reference [16]. It is well accepted that the mesh quality has signicant inuences on the solutions of the partial dierential equations (PDE) regardless of the numerical method. According to the ∗ Correspondence to: Yaoxin Zhang, National Center for Computational Hydroscience and Engineering, The University of Mississippi, P.O. Box 1500, Oxford, MS 38677, U.S.A. † E-mail: yzhang@ncche.olemiss.edu ‡ Post-doctoral Research Associate. § Research Associate Professor. ¶ Assistant Director for Basic Research. ‖ F.A.P. Barnard Distinguished Professor. ∗∗ Director. Contract=grant sponsor: USDA Agriculture Research Service; contract=grant number: 58-6408-2-0062 Contract=grant sponsor: The University of Mississippi Received 9 August 2005 Revised 7 November 2005 Copyright ? 2006 John Wiley & Sons, Ltd. Accepted 7 November 2005