Study On The Constrained Quadrilateral Mesh Generation Based On Paving

The numerical methods including the finite element method and finite volume method have been widely used in all kinds of engineering analysis.The mesh generation has been one of the key steps for the application of these numerical methods.Over the past few decades,with various mesh generation methods proposed and a lot of commercial mesh generation software developed,the mesh generation technology has made great progress and become quite mature.In the numerical analysis of some fields,there are usually many constraints in the model,such as constraint lines,constraint points,and local refinement etc.These constraints may represent the common boundaries between neighbor sub-regions,the location of load or boundary conditions imposed or the local area of stress concentration or crack propagation.When generating the mesh,these constraints must be taken into account,and the mesh nodes are should be attached to these constraints.The existing methods and software usually cannot directly deal with the model with internal constraints.In order to process these constraints,artificial methods are needed to decompose the model into sub-regions,then mesh generation can be carried out in each sub-region.However,the artificial process will be a tedious and heavy task when there are a lot of constraints in the region.Therefore,an automatic method is necessary to process the internal constraints and realize the mesh generation automation in the region and improve the efficiency of numerical analysis.In this thesis,the method of quadrilateral mesh generation with complicated constraints is presented for the flood evolution analysis and floor design analysis in which a lot of constraints always exist.The algorithm for automatic process of constraints is proposed,and the corresponding mesh generation program is developed,which has achieved good results in practical application.The first section of this paper provides a general overview of the mesh generation technology development and the current research status of the constrained mesh generation.On the basis of advantages and disadvantages comparison of various mesh generation methods,the Paving method is chosen to generate two-dimensional quadrilateral mesh.But there are a few shortcomings in the practical application.In this paper,the original Paving algorithm is improved in order to enhance the quality and reliability of mesh generation.The Pattern method is used to generate mesh near sharp and narrow area to avoid the generation of low quality mesh.An effective control method is proposed to solve the problem of the row mesh generation without ending.The new criteria for wedge insertion and tuck formation is presented,which can be not only applicable to uniform mesh size but also to non-uniform mesh size.When there are sub-regions bounded by constraint lines,the region can be decomposed into a series of sub-regions,and then the quadrilateral mesh can be generated in each sub-region.The automatic algorithm for sub-regions decomposition is given making that sub-regions can be determined automatically without any user interaction by this method.A sub-region is defined by its boundaries,and may still have constraint lines in it,but these constraint lines cannot form closed regions,and no sub-regions are allowed to exist inside a sub-region.After a region is decomposed into several sub-regions,the time of intersection judgment will be reduced,so By the sub-region decomposition,the total time of mesh generation will be cut down owing to the intersection judgement decrease.The methods to handle constraint lines and constraint points are given.The constraint lines are looked as the holes with zero area.A novel algorithm for constructing loops from constraint lines is proposed and suitable for any distribution of constraint lines.The constraint points can be processed as constraint lines and quality elements can be generated around constraint points.Based on Paving method,the program for 2-D quadrilateral mesh generation with feature constraints using C++ language has been developed and applied to flood analysis system and floor design system.Several examples for mesh generation with feature constraint are given to demonstrate the reliability of the algorithm presented paper and its application in actual engineering analysis.