The mesh generation

The manoeuvre generation fall upon general methods ( unified, unstructured, hybrid, adaptive, etc.) and discuss their key features and applicationsA key musical note of the bounded element method for numerical computation is lock in generation. One is given a domain (such as a polygon or polyhedron more(prenominal) vivid versions of the problem completelyow curved domain boundaries) and must partition it into simple elements meeting in well-defined ways. There should be few elements, but many portions of the domain may need small elements so that the computation is more accurate in that respect. All elements should be well shaped (which means different things in different situations, but primarily involves bounds on the angles or aspect ratio of the elements). One distinguishes structured and unstructured meshes by the way the elements meet a structured mesh is one in which the elements have the network network topology of a regular grid. Structured meshes argon typically easier to compute with (saving a constant compute in runtime) but may require more elements or worse-shaped elements. Unstructured meshes are often computed using quadtrees, or by Delaunay triangulation of point sets however there are quite varied get downes for selecting the points to be triangulatedThe simplest algorithms directly compute nodal placement from some given function. These algorithms are referred to as algebraic algorithms. Many of the algorithms for the generation of structured meshes are desc decisionents of numerical grid generation algorithms, in which a differential equation is single-minded to determine the nodal placement of the grid. In many cases, the outline cleard is an elliptic system, so these methods are often referred to as elliptic methods.It is difficult make general statements about unstructured mesh generation algorithms because the most adult methods are very different in nature. The most popular family of algorithms is those based upon Dela unay triangulation, but other methods, such as quadtree/octree approaches are also used.Delaunay MethodsMany of the unremarkably used unstructured mesh generation techniques are based upon the properties of the Delaunay triangulation and its dual, the Voronoi diagram. Given a set of points in a plane, a Delaunay triangulation of these points is the set of triangles such that no point is inside the circumcircle of a triangle. The triangulation is unique if no terzetto points are on the said(prenominal) line and no four points are on the same circle. A similar definition holds for higher dimensions, with tetrahedral replacing triangles in 3D.Quadtree/Octree MethodsMesh adaptation, often referred to as Adaptive Mesh Refinement (AMR), refers to the modification of an existing mesh so as to accurately capture die hard features. Generally, the goal of these modifications is to improve resolve of flow features without excessive increase in computational effort. We shall discuss in bri ef on some of the concepts important in mesh adaptation.Mesh adaptation strategies stub usually be classified as one of three general types r- civilisation, h-refinement, or p-refinement. Combinations of these are also possible, for example hp-refinement and hr-refinement. We summarise these types of refinement below.r-refinement is the modification of mesh resolution without changing the number of nodes or cells present in a mesh or the connectivity of a mesh. The increase in resolution is made by moving the grid points into regions of activity, which results in a greater glob of points in those regions. The movement of the nodes house be controlled in various ways. On common technique is to treat the mesh as if it is an elastic solid and solve a system equations (suject to some forcing) that deforms the original mesh. Care must be taken, however, that no problems due to excessive grid skewness arise.h-refinement is the modification of mesh resolution by changing the mesh connec tivity. Depending upon the technique used, this may not result in a change in the overall number of grid cells or grid points. The simplest strategy for this type of refinement subdivides cells, while more complex procedures may insert or remove nodes (or cells) to change the overall mesh topology.In the component case, either parent cell is divided into barbarian cells. The choice of which cells are to be divided is summarizeressed below. For every parent cell, a new-fangled point is instituteed on each face. For 2-D quadrilaterals, a new point is added at the cell centroid also. On joining these points, we get 4 new child cells. Thus, every quad parent gives rise to four new offsprings. The advantage of such a procedure is that the overall mesh topology remains the same (with the child cells taking the place of the parent cell in the connectivity arrangement). The subdivision process is similar for a angulate parent cell, as shown below. It is easy to see that the subdivisi on process increases both the number of points and the number of cellsA very popular tool in exhaustible Element Modelling (FEM) rather than in Finite Volume Modelling (FVM), it achieves change magnitude resolution by increasing the order of accuracy of the polynomial in each element (or cell).In AMR, the selction of parent cells to be divided is made on the basis of regions where there is appreci qualified flow activity. It is well known that in compressible flows, the major features would include Shocks, Boundary Layers and rob Layers, Vortex flows, Mach Stem , Expansion fans and the like. It can also be seen that each feature has some physical signature that can be numerically exploited. For eg. shocks continuously involve a density/pressure jump and can be detected by their gradients, whereas boundary layers are always related with rotationality and hence can be dtected using curl of velocity. In compressible flows, the velocity divergence, which is a measure of compressibl ity is also a favourable choice for shocks and expansions. These sensing paramters which can indicate regions of flow where there are activity are referred to as ERROR INDICATORS and are very popular in AMR for CFD.Just as refinement is possible by ERROR INDICATORS as mentioned above, certain other issues also assume relevance. Error Indicators do detect regions for refinement, they do not actually tell if the resolution is good enough at any given time. In fact the issue is very severe for shocks, the smaller the cell, the higher the gradient and the indicator would keep on picking the region, unless a threshold value is provided. Further, many users make use of conservative values while refining a domain and in general end up in refining more than the essential portion of the grid, though not the complete domain. These refined regions are unneccesary and are in strictest sense, contribute to unneccesary computational effort. It is at this juncture, that reliable and resonable me asure of cell error become necessary to do the process of coarsening, which would reduce the above-said unnecessary refinement, with a view towards generatin an optimal mesh. The measures are given by sensors referred to as ERROR ESTIMATORS, literature on which is in abandunce in FEM, though these are very rare in FVM. retard of the refinement and/or coarsening via the error indicators is often undertaken by using either the solution gradient or soultion curvature. Hence the refinement variable coupled with the refinement method and its limits all need to be considered when applying mesh adaptationA hybrid model contains two or more subsurface layers of hexahedral elements. Tetrahedral elements fill the interior. The intonation between subsurface hexahedral and interior tetrahedral elements is made using degenerate hexahedral (pyramid) elements.High flavour stress results demand high quality elements, i.e., aspect ratios and internal angles as close to 11 and 90, respectively, as possible. High quality elements are particularly important at the surface. To accommodate features within a component, the quality of elements at the surface of a hexahedral model generally suffers, e.g., they are skewed. Mating components, when node-to-node contact is desired, can also adversely affect the models element quality. Even more difficult is producing a tetrahedral model that contains high quality subsurface elements. In a hybrid model, the hexahedral elements are only affected by the surface mesh, so creating high quality elements is easy.Minimal effort is required to convert CAD data into surface grids using the automated processes of pro-surf. These surface grids are read by pro-am. The surface grid is used to extrude the subsurface hexahedral elements. The thickness of each extruded element is controlled so that high quality elements are generated. The interior is filled mechanically with tetrahedral elements. The pyramid elements that make the transition are also g enerated automatically.A hybrid model will generally contain many more elements than an all-hexahedral model olibanum increasing analysis run-time. However, the time saved in the model construction phase the more labor intensive phase more than makes up for the increased run-time. Overall project time is reduced considerably. Also, as computing power increases, this disadvantage will eventually disappear.Hexahedral MeshingANSYS Meshing provides multiple methods to generate a pure hex or hex dominant mesh. Depending on the model complexity, desired mesh quality and type, and how much time a user is able to spend meshing, a user has a scalable solution to generate a quick automatic hex or hex dominant mesh, or a highly controlled hex mesh for optimal solution efficiency and accuracy.Mesh MethodsAutomated Sweep meshingSweepable bodies are automatically detected and engaged with hex mesh when possibleEdge increment assignment and side matching/mapping is done automaticallySweep path s found automatically for all regions/bodies in a multibody partDefined inflation is swept through connected swept bodiesUser can add surface controls, mapped controls , and select ejaculate faces to modify and take control over the automated sweepingAdding/Modifying geometry slices/decomposition to the model also greatly aids in the automation of getting a pure hex mesh.Thin Solid Sweep meshingThis mesh method apace generates a hex mesh for thin solid split that have multiple faces as source and target.Can be used in conjunction with other mesh methodsUser can add sizing controls, mapped controls, and select source faces to modify and take control over the automated sweepingMultiZone Sweep meshingThis advanced sweeping approach uses automated topology decomposition behind the scenes to attempt to automatically create a pure hex or mostly hex mesh on complicated geometriesDecomposed topology is meshed with a mapped mesh or a swept mesh if possible. A user has the option to allow for free mesh in sub-topologies that careen be mapped or swept.Supports multiple source/target selectionDefined inflation is swept through connected swept bodiesUser can add sizing controls, mapped controls and select source faces to modify and take control over the automated meshingHex-dominant meshingThis mesh method uses an unstructured meshing approach to generate a quad dominant surface mesh and then fill it with a hex dominant meshThis approach generally gives straitlaced hex elements on the boundary of a chunky part with a hybrid hex, prism, pyramid, test mesh internallyTetrahedral MeshingThe combination of robust and automated surface, inflation and tet meshing using default physics controls to ensure a high-quality mesh suitable for the defined simulation allows for push-button meshing. Local control for sizing, matching, mapping, virtual topology, misgiving and other controls provide additional flexibility, if needed.Mesh Methods firearm conforming mesh methodBottom-up approach (creates surface mesh, then volume mesh)Multiple triangular surface meshing algorithms are employed behind the scenes to ensure a high quality surface mesh is generated, the first timeFrom that inflation layers can be grown using several techniquesThe remaining volume is meshed with a Delaunay-Advancing Front approach which combines the speed of a Delaunay approach with the smooth-transitioned mesh of an march on front approachThroughout this meshing process are advanced size functions that maintain control over the refinement, smoothness and quality of the meshPatch independent mesh methodTop-down approach (creates volume mesh and extracts surface mesh from boundaries)Many common problems with meshing occur from grownup geometry, if the bad geometry is used as the basis to create the surface mesh, the mesh will often be bad (bad quality, connectivity, etc.)The patch independent method uses the geometry only to associate the boundary faces of the mesh to the regions of i nterest thereby ignoring gaps, overlaps and other issues that give other meshing tools countless problems.Inflation is done as a post step into the volume mesh. Since the volume mesh already exists, collisions and other common problems for inflation are known ahead of time.Note For volume meshing, a tetrahedral mesh generally provides a more automatic solution with the ability to add mesh controls to improve the accuracy in critical regions. On the contrary, a hexahedral mesh generally provides a more accurate solution, but is more difficult to generate.Shell and Beam MeshingFor 2-D planar (axisymmetric), shell and beam models, ANSYS Meshing provides efficient tools for quickly generating a high quality mesh to accurately simplify the physics.Mesh Methods for shell modelsDefault surface meshingMultiple surface meshing engines are used behind the scenes to provide a robust, automated surface mesh consisting of all quad, quad dominant or all tri surface mesh.User can add sizing contro ls, and mapped controls to modify and take control over the automated meshingUniform surface meshingOrthogonal, uniform meshing algorithm that attempts to armament an all quad or quad dominant surface mesh that ignores small features to provide optimum control over the edge lengthDescribe key features of ALL existing meshing options in Ansys Mesh module and discuss their applicationsThe meshing tools in ANSYS Workbench were designed to follow some directional principlesParametric Parameters drive systemPersistent Model updates passed through systemHighly-automated Baseline simulation w/limited inputFlexible Able to add additional control w/out complicating the workflowPhysics aware Key off physics to automate modelling and simulation throughout systemAdaptive architecture Open system that can be tied to a customers processCAD neutral, meshing neutral, solver neutral, etc.By compound best in class meshing technology into a simulation driven workflow, ANSYS Meshing provides a next generation meshing solution.