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Developments and trends in three-dimensional mesh generation. (English) Zbl 0675.65120

The object of the paper is a review of diverse numerical methods for the generation of various meshes for solving complicated partial differential problems in three-dimensional shapes. The main interest is concentrated to methods for calculating a transonic flow over airfoils. Following methods for the mesh generation are considered: Numerical techniques based on transformation from physical coordinates to another coordinate system; algebraic methods based on multi-surface fitting, transfinite interpolation, sequential mapping and grid blending.
For the handling of complicated geometries while maintaining adequate control over the mesh point distribution and the cell shape a multiblock structure is introduced and recommended. For the interference of separate meshes for each component overlapped, patched and composite methods are considered. Triangulation methods for mesh construction are also described and the influence of the mesh type to the accuracy of the solution is examined. Adaptive procedures for mesh redistribution and mesh enrichment are suggested.
Reviewer: J.Vaníček

MSC:

65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
76H05 Transonic flows
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
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