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Constrained Unstructured Mesh Generation

Posted on:2010-07-07Degree:DoctorType:Dissertation
Country:ChinaCandidate:S X WangFull Text:PDF
GTID:1100360305482660Subject:Computational Mathematics
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As a carrier of numerical simulation and analysis, mesh generation is one of the essential technical steps in the field of scientific and engineering computing. Mesh quality affects the numerical accuracy, and poor grid often leads to the failure of numerical simulation.Without structural constraints of nodes, it's easy and flexible to control the unit size, shape, and location of the points in the unstructured mesh. According to the scale function and the calculating requirements, we can get rational unit distributions for the field. It's convenient to generate unstructured mesh on complex shape of computational field and solve discontinue problems adaptively, which can improve the numerical accuracy.With practical application of unstructured grid in mind, we try to solve the constrained unstructured mesh generation in 2D and 3D. The innovations are:(1) Three methods are presented to generate 2D constrained unstructured mesh without adding Steiner points, and these methods can generate constrained mesh for arbitrary field in 2D.(2) A constrained boundary recovery method for 3D mesh is obtained through perturbing Steiner points unilaterally and triangulation method by vector boundaries advancing (TMVBA), and A 3D constrained unstructured mesh generation method is obtained through perturbing Steiner points bilaterally and TMVBA.(3) A new method for constrained boundary recovery in mesh generation is studied, which combines the advantage of the advanced front method and conforming Delaunay method.(4) The scale function is optimized by solving ODEs by analysizing the boundary curvature, axis and smooth between adjacent points.(5) The unstructured mesh is generated by weak domain indicating function (WDIF).The detailed works:(1) The generation of 2D constrained unstructured mesh. In this thesis we present three methods to generate 2D constrained unstructured mesh:a) triangulation method by vector boundaries advancing (TMVBA),b) constrained Delaunay mesh generation based on local reconstruction,c) constrained Delaunay mesh generation based on side-swapping. TMVBA could triangulate any closed domain without coordinate transformation, and the last two methods can triangulate plane domain without boundary orientation. The convergence and stability of these three methods are proved.(2) The generation of 3D constrained unstructured mesh. We achieve this goal in three steps:a) A conforming mesh generation method is obtained by combining TMVBA and adding Steiner points into the Delaunay mesh structure, which can preserve the shape of the field.b) A constrained boundary recovery for three dimensional Delaunay triangulations is obtained through moving all points apart from constrained sides and faces by unilaterally perturbing Steiner points (UPSP) and retriangulating the constrained faces by TMVBA. The advantage of this approach is no Steiner point needed.c) A constrained recovery for three dimensional Delaunay triangulations is obtained through moving all points apart from constrained sides and faces by bilaterally perturbing Steiner points (BPSP) and retriangulating the constrained faces by TMVBA. The advantages of this approach are that no boundary orientation is needed and that all constrained faces and sizes are recovered.The convergence and stability of these methods are proved.(3) A new method for constrained boundary recovery in mesh generation is studied. This method is a combination of advancing front method and conforming Delaunay method. This new methods exerts all the advantages of advancing front method and conforming Delaunay method, while avoiding the disadvantages of them. Here we triangulate the remanent domain on the advanced front of water-tight mesh by conforming Delaunay method, and then couple the two meshes at Steiner points.(4) In 2D, we optimize scale function by analyze the boundary curvature, axis and smooth between adjacent points to make it much smoother.(5) For the field described by implicit function, we first deduct WDIF to describe it, and prove the existence and multiplicity of WDIF. Then, we generate the unstructured mesh by it. Lastly, we generalize this method to adaptive mesh.In the thesis, we employ the probability filer method to distribute mesh points, optimize the location of points and structure of mesh by Spring and side swapping (side-face flip) respectively. The side eating means could get rid of all the bad-shaped elements from mesh.
Keywords/Search Tags:unstructured mesh, constrained, boundary recovery, Delaunay, optimization, scale, advancing front method
PDF Full Text Request
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