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Mesh Generation Using Re-meshing Method

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Mesh generation using re-meshing method has also been extensively used for aerospace moving body applications. Thompson et. al. has implemented an efficient method with the algebraic scheme transfinite interpolation which is capa- ble to generate three-dimensional moving mesh. Gaitonde and Fiddes adopted algebric method to generate deforming grids for the unsteady simulation of a wing configuration for transonic flow. Exponential blending function has been employed to increase the robustness and quality of the grid. Later on, Reuther et al. used similar approach with adjoint formulation for complex aircraft aerodynamic shape optimization and their work has been extended for full aircraft aeroelasticity by Byun and Guruswamy. Despite of several implementation for improving the re- meshing scheme, this method has been found less accurate and expensive for large unstructured grids. Apart from re-meshing, immersed boundary method and overset mesh technique, the mesh deformation has also attracted researchers’ with wide range application due to its highly costomised control, robustness and quality mesh generation ca- pability.

Grid deformation technique is also popular because the re-meshing and interplation is very expensive. Deforming mesh is only technique which can handle the contoneous deforming surface. There are three types of schemes available for mesh deformation namely physical analogy, iterative smoothing and algebric tech-Batina et. al. have considered all outer nodes as fixed and inner nodes were moved based on the motion defined on the moving bound- ary, and new positions of nodes were obtained performing the static equilibrium in all three directions. The mesh nodes were moved with maintaining the same node connections and considering all internal nodes as set of springs with defined stiffness as inversely propotional to the length of edge. The discretization of equations of deforming mesh system mesh deformed at each time-step instead of regenerating the whole mesh. However, this method is not suitable for viscous flow mesh with large displacement. Negative cell volume has been a measure issue for refined boundary meshes. Farhat et. al. has implemented the torsional spring analogy to avoid the peneteration of triangle with neighbouring traiangles and found success in deform- ing mesh with greater robustness and quality. Further, spring analogy has been validated with consideration of two types of springs namely vertex spring analogy and segment spring analogy by Blom et. al.

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The node collision is prevented by defining stiffness as inverse of the segment length. The similarity between elliptic grid generation and the spring analogy is also investigated. The inversion of tri- angular elements prevented with principle of Saint Venant in boundary correction using semi torsional springs. Murayama et. al. has proposed a simple robust method to avoid squashed invalid element generation with consideration of each elemental shape for the three- dimensional moving and deforming unstructured grid. It has been tested and demon- strateed for its improved robustness without significant increase in computational cost. The method has also been demonstrated for the tail-fuselage juncture region andfound suitable for aircraft control surfaces. Apart from previously discussed, elastic analogy and spring analogy has also been discused by several workers’. However, the most common is all proposed method is that in spring analogy, the positions of internal nodes are obtained by static equilibrium.

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