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发表于 2003-5-14 20:45:49
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《笛卡尔网格生成方法概述》，它将是非结构网格生成方法之后的又一热点！欢迎讨论！
Followed are part of Dr.Alpesh Patel's Phd thesis, which review the mesh generation techiques. I hope you could be intereseted.
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Structured grid technology is by far the most widespread meshing technique in the CFD community. Such grids are characterized by the fact that each mesh point can be indexed by three integers. These meshes, made of consecutive hexahedral cells, offer a significant advantage in terms of computational costs. Indeed, each repeated operation in the code can be formulated in organized loops over the indices, so that simple and efficient schemes can be easily constructed.
However, the application of this technology to flow simulation around complex geometries such as complete cars or aircrafts is very difficult since the computational domain is often multiply connexed. Furthermore, for many practical problems, the solution does not contain a single length scale, but instead includes flow features like shocks, boundary layers, vortices and regions where the dominant length scale can be orders-of-magnitude smaller than that of the main flow. This poses a great challenge
to structured grid technology because of the difficulty in adequately clustering points where needed.
These problems can be partially solved by resorting to a multi-block method [78][70], which divides the computational domain into hexahedral blocks that are meshed separately, with the possibility of having full non-matching connections between blocks. This approach is quite popular, since it is a straightforward generalization of structured grid technology, and the programmer need only pay attention to the treatment of non-matching connections between blocks. However, the topological decomposition of the domain into blocks can become extremely complicated, and automatic decomposition is still far from being realizable. Therefore, multi-block
structured mesh generation around a complex geometry may require weeks, even for experienced users, and is thus not the most appropriate method for meshing complex computational domains.
An alternative is to resort to Chimera grids. In this case, no domain decomposition is needed, as separate meshes are generated around all geometric entities, and the grids are overlaid on each other. Their generation is however not as straightforward as it appears, since overlapping meshes of very different local resolution have to be avoided
to prevent large interpolation errors. Furthermore, a more complex data structure is required to handle the transfer of information between the overlapping grids. The maintenance of the conservation property of the numerical methods, as well as numerical diffusion resulting from interpolation operations are other important issues to be addressed. This technique has been used in e.g. [103], [192].
The most promising approach is unstructured grid technology. Such meshes do not involve any natural structure. Therefore, the vertices cannot be referenced by global indices as in structured grids, since the local mesh configuration differs from one vertex to another. This approach offers many advantages since quasi-automatic mesh generation algorithms can be developed. Furthermore, it is possible, by using a mesh adaptation procedure to cluster grid points where required by geometry particularities
and/or flow physics, thereby optimizing computational costs with respect to accuracy.
The approach mostly followed in unstructured grid technology consists in using meshes involving tetrahedra, essentially because of the availability of algorithms to automatically generate these meshes for complicated geometries. Actually, one can distinguish two classes of tetrahedral mesh generation algorithms: the Delaunay approach [49] and the advancing front method [123]. In the first approach, points are introduced in an existing grid in order to meet a certain criterion corresponding to, for instance, characteristic sizes. The grid is then locally reconnected in order to satisfy a mathematical criterion [13]. In the advancing front method, the mesh is created by starting from a distribution of points at the boundaries. This set of points is used as initial front. A vertex is then added to create a new tetrahedron, whose faces serve to define an updated front. The procedure is repeated until the whole domain is filled with
tetrahedra.
Nevertheless, for high-Reynolds number viscous flow simulations, the number of tetrahedra required for the accurate resolution of boundary layers grows significantly. Furthermore the use of tetrahedra degrades the accuracy of classical numerical methods. This problem has been partly resolved by resorting to hybrid grids combining prisms in boundary layers and tetrahedra outside, [98].
Another popular approach is the Cartesian grid generation method [1][2], where hexahedral meshes are generated by octree subdivision of one hexahedral cell. Such technique has received increasing interest for its ability to easily generate meshes around complex geometries. Special attention, however, should be paid to so-called cut-cells that intersect the bodies. Indeed, since the arbitrary nature of geometric intersection implies that these cells may be orders-of-magnitude smaller than their
neighboring cells, they can impose a great burden on the numerical discretization.Research into these cut-cell issues has been performed by many authors, see e.g.[18][33][62].
However, cartesian grid generation is not suited for high-Reynolds number viscous flow computations because of the isotropic behavior of Octree-refined meshes. An alternative is again to resort to a hybrid of different grid types, which is done in the socalled Hybrid-Cartesian approaches used by Delanaye et al. [44], and by Deister et al.,[41], [42]. The principle of the method is to generate a quasi-prismatic grid in nearbody regions by marching the body surface triangulation outwards. A cartesian mesh
is then generated to fill the rest of the computational domain. Cut-cells are this time met at the intersections between the cartesian grid and the quasi-prismatic region.
The possibility of using body-fitted all-hexahedra unstructured meshes is however more appealing. Compared to tetrahedral and hybrid grids, the same resolution is achieved with less elements, since hexahedra can combine five to six tetrahedra, or two prisms. Furthermore, their use guarantees the accuracy of numerical methods, especially compared to tetrahedral grids. Compared to cartesian and hybrid-cartesian grids, the main advantage is that all-hexahedra body fitted meshes do not require any
particular numerical treatment at boundaries or at the intersection between the inviscid cartesian mesh and the quasi-prismatic viscous mesh, since no cut-cells are generated.
In addition, using hexahedra in the boundary layer enables the reduction of the number of elements by a factor two, to achieve the same grid clustering as a prismatic mesh.
However, very few applications of all-hexahedra body-fitted meshes have been presented so far in the literature, mainly because of the great difficulty of devising automatic grid generation algorithms. Recently, a new body-conforming Octree mesh generation technique has been proposed by several authors, [179][200][201], and adopted by NUMECA International for the development of its new unstructured grid generator, HEXPRESSTM, [179][45]. The mesh generation method takes as input a computational domain defined by its topology and its geometry, the latter being represented by a set of triangulations. An initial cartesian mesh is anisotropically
refined until the cell sizes match the typical length scales of the geometry. Surface geometry is intersected with the non-body adapted mesh, and the cells located outside or intersecting the computational domain are removed. The remaining staircase mesh is then snapped onto the geometry. Discrete features, such as sharp trailing edges of wings, are recovered by sophisticated algorithms. Mesh quality in the vicinity of the surface geometry is improved by adding buffers of high-quality hexahedral cells and
by applying a combination of mesh untangling and optimization, [108]. Finaly,viscous layers are created by anisotropically refining the buffer layer, and redistributing points so that a prescribed first layer cell size and a geometric progression of the stretching ratio are achieved.
This new approach to grid generation is a promising avenue to automate viscous flow simulation involving very complex geometries, consisting, for instance, of complete aircrafts with flaps and engines. It combines the advantages of other unstructured grid techniques - generation time and mesh adaptation capability -, while removing some of their drawbacks, by automatically producing high quality, possibly stretched hexahedral cells.
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