Based On The Principle Of Optimization Of Element Size Field Smoothing:Model And Application

Mesh generation is the pre-processing of the finite element analysis and is also a main performance bottleneck. In order to control the scale of the grid and ensure the accuracy of the subsequent analysis, the grid generation algorithm needs to use the element size function to arrange size unit in different positions of the problem area to adapt the variations of geometry features and physical gradient in problem domain.Given the initial unit size field usually does not meet requirements of smoothing transition, distance near the point unit size value is very different, during which will unavoidably produce poor quality grid unit. Therefore, element size field smoothing is an important subject of finite element mesh generation research.The existing methods mainly use the Cartesian background grid to define the size field, having some defects, such as the existence of background grid scale is too large.The corresponding algorithm space-time efficiency poorly. Based on the characteristics of unstructured grid automatic and adaptive generation capacity, this paper choose the unstructured background mesh to define the size field and studies the corresponding size field smoothing methods. The main work includes two aspects:Firstly, based on reasonable basic assumptions, element size field in the linear domain and triangular domain transition controlled mathematical conditions extended to the tetrahedral domain. Then, with the goal of minimizing the variation of the size field, the optimization model of the smoothing problem of the size field is established by the control of the size field in the three-dimensional domain transition. The existence of the convexity and the only optimal solution of the model is proved.Secondly, based on the interior point method, numerical algorithm of the optimization model is developed and the algorithm is applied to geometric adaptive size field smoothing. Combined with initial geometric adaptive size field calculation,Delaunay grid generation algorithm, to achieve a set of geometry adaptive tetrahedral mesh automatic generation of software flow.Numerical experiments show that, and the existing methods are also based on classical method of unstructured background grids, the new method successfully solves some defects that such as H-correction method can not guarantee smoothing transition of element size field in the background grid (resulting in final grid containing a certain number of low quality transition unite), and GradH-Correction algorithm to change initial size field is too intense (resulting in a large range of the final grid unit"excessive refinement").