Study On The Optimization Of The Quality Of Quadrilateral Mesh

The quality of the mesh has great influence on the accuracy and convergence of numerical simulation of finite element and finite volume.Automatic mesh generation method,such as octree algorithm,advancing front technique and paving method,will inevitably produce poor quality element or even illegal element during the generation of mesh,results in the decrease of numerical calculation accuracy and the analysis process discontinued.In order to improve the accuracy of numerical simulation, it is necessary to optimize the finite element mesh to improve the quality of the mesh.This paper carrying out a research of the quadrilateral mesh quality optimization method from two aspects of node location optimization and the grid topology optimization,developed the corresponding mesh optimization program, and apply to the actual mesh generation of 2D flood analysis.On the premise of the mesh topology unchanged,we can improve the quality of the grid by move the position of it’s nodes.Using Laplacian smoothing algorithm to smooth the mesh is the most commonly used mesh quality optimization method.However, Laplacian smoothing algorithm may cause unit reverse and also cause the case of nodes moved to the outside boundary in the treatment of the concave area unit. Aiming at the existing problem of Laplace algorithm, a new method for the optimization of node location set up is proposed in this paper, based on the steepest descent method,set up grid quality optimization objective function, the node location as design variables, by optimizing the node position, to achieve goal of improving the quality of the grid.Compared to Laplacian smoothing algorithm, based on node location optimization method, in the treatment of the concave area won’t appear unit reversal, concave area grid quality is guaranteed.As to the nodes angle in the grid which is too big or too small,such as along border unit angle close to 180 。 and the unit node has the number of unit around internal nodes (or valence) is greater than 5 or less than 3, it is difficult to improve the quality of the grid by the method of simple move node location,it is necessary to adopt the method of topology optimization,namely change the connection unit nodes, to improve the quality of the grid.This paper proposed topology optimization method based on boundary optimization, shape optimization, connectivity optimization and size optimization.As to boundary optimization, aimed at unit on the border close to the triangle unit, the method is proposed about merging boudary element and adjiacent element,and then to merge in accordance with the local grid set template method to regenerate, can eliminate the boundary unit close to the triangle unit.As to shape optimization, aimed at the poor quality of the internal units which have the angle more than 160。 and illegal units, it is proposed to merge the large angle unit with the big angle of the adjacent units and regenerated method, can eliminate the large angle unit and illegal unit.In terms of connectivity optimization, summarizes the various node connectivity model,according to the objective node valence and the node valence around the objective node, matching the existing model, by changing the node connectivity of the unit, make each node valence close to ideal value (internal nodes is 4) and improve the quality of the grid.In terms of size optimization, in view of the grid unit in the ratio of the longest and shortest while excessive, through a merger with adjacent units, change the diagonal position of the hexagon area or break hexagon area into three units, which can effectively reduce the size of the grid difference, improve the quality of the grid.On the basis of proposed node location optimization and topology optimization, using C++language write quadrilateral mesh quality optimization program on VS2012 platform,and optimize the actual quadrilateral mesh, the results show that the optimization method proposed in this paper can effectively eliminate the poor quality of the unit, significantly improve the quality of the grid.