Solid modeling (required to create 3D geometry) and mesh generation are at present separate steps, performed using different programs and software environment, and a greater seamless integration is still in distant future. The first step of meshing is to ensure the "topological consistency" of the 3D geometry when the data is transferred from "Solid Modeling" environment or "mesh generation" environment. The topology refers to the way points, lines and surfaces connect to form a three-dimensional space.
This step involves division of the computational domain into small sub-divisions called a grid or mesh of cells/elements/control volumes. The 2D boundaries of this smaller (discretized) domains are called Faces, the 1D boundaries are called Edges and 0-D boundaries are called Nodes or Vertices. The solution of flow problems are defined at the nodes of the cells. In general, the accuracy of CFD simulation is governed by cell size. Finer the mesh (lower the cell size), better is the result. However, the hardware resource increase with increase in no. of cells (elements) in the mesh. Hence, a trade-off is required.
A wedge or prism element is normally created by slicing a tetrahedron parallel to its base. Since, this element is created by rule near the boundaries namely of type walls, they will appear triangles from one side and quadrilateral from other side.
The elements defining the flow domains other than boundaries are called interior elements. Note that the mesh topology used to specify simulation parameters may be different than the mesh topology internally created by the solver. For example, a solver may create a mesh around each node by connecting the centroids of all the elements associated with it. This is called a vertex-based scheme (e.g. CFX). In some cases, the mesh supplied to the solver will be used as provided such as FLUENT. This is known as cell-centred scheme.
Hanging nodes are considered crack in FE solvers for structural simulations. However, hanging nodes are acceptable in most of of the CFD solvers and FLUENT even has a method of mesh adaption based on handing nodes creation.
Mesh Generation Process: the two broadest categories of mesh are (a)structured mesh and (b)unstructured mesh. As the names suggest, structured mesh has a unique, predictable and repeatable topology whereas unstructured mesh is a pseudo-random distribution of element in space. Strcuctured meshes are composed of either quadrilaterals or hexahedrals. Unstrctured mesh can be a combination of all types of elements. Yet, a mesh consisting of only hexahedrals can also be unstructured mesh.
There are various mesh generation algorithms available in industry: OCTREE (QUADTREE), Delaunay, Advancing Front, Directed Meshing (Swept Meshing), Cut-Cell or Cartesion or snappyHexMesh, Paving, Multi-zone, Hexa-core ... to name few. Directed meshing techniques work on extrudable geometry: this refers to shapes which can be generated by linear (translational) and rotational or combination of both operation on a lower dimension geometry to get a higher dimension geometry. For example, a frustum is a linear extrusion of circular disk in radial as well as tangential direction, a cylinder is a uniform extrusion of circular disk, a circular disk is rotational extrusion of a line about one of its ends. The extrusion process is also known as sweeping or lofting operation.
a non-manifold geometry or 3D shape cannot be unfolded into a 2D surface with all its normals pointing the same direction. In other words, a 3D model can be represented digitally but there is no geometry which can physically support it in the real world. In the following picture, a hexahedral element has internal tetrahedral element which is not necessary at all.
Similarly, if a vertex is attached to the interior of a surface or if surrounded by a volume but not connected with any of the edges defining that volume, it is called a non-manifold vertex.
Recommendation from ANSYS FLUENT: For any other software, it is recommended to check the rating scale. For example, ICEM CFD considers skewness of 1.0 as perfect and scale is exactly opposite to that of FLUENT.
|Skewness||0||0 ~ 0.25||0.25 ~ 0.50||0.50 ~ 0.75||0.75 ~ 0.95||0.95 ~ 1.00||1.00|
Verbatim copy form ANSYS FLUENT 12.0/12.1 Documentation: Skewness is defined as the difference between the shape of the cell and the shape of an equilateral cell of equivalent volume. Highly skewed cells can decrease accuracy and destabilize the solution. For example, optimal quadrilateral meshes will have vertex angles close to 90°, while triangular meshes should preferably have angles of close to 60° and have all angles less than 90°.
Verbatim copy form ANSYS FLUENT 12.0/12.1 Documentation: Aspect ratio is a measure of the stretching of the cell. For highly anisotropic flows, extreme aspect ratios may yield accurate results with fewer cells.
A mesh consisting of more than 1 element types such as tetrahedrons and hexahedrons are called hybrid. They may or may not be conformal. In case a hybrid mesh consisting of tetrahedrons and hexahedrons are conformal, pyramid elements need to be used to transition from tetra to hexa elements.A non-conformal mesh has grid nodes which do not match up along an interface. This type of mesh is useful for design study where parts can be replaced without regeneration of the entire mesh. Sometimes, this type of mesh becomes a necessity for meshing complex geometries. Recommended approach to have number of nodes / elements in the ratio 2:1 or less on the two sides of a non-conformal interface.
For complex geometries such as engine under-hood thermal management, structured mesh quad/hex meshes are neither possible nor show any numerical advantage, thus one can save meshing effort by using a mesh consisting of tri/tetra elements.
Mesh skewness reduces the accuracy of face integrals (calculation of face flux) since the interpolated face value does not lie in the center of the face F, but instead lies at the intersection of vector joining cell centres and the common face, denoted by R above.
Warp: It applies only to quadrilateral elements and is defined as the variation of normals between the two triangular faces that can be constructed from the quadrilateral face. Warp value is the maximum of the two possible ways triangles can be created in a quadrilateral/rectangular face.Various checks required to ensure the geometrical and topological consistency of a mesh is completely described by the options available in ANSYS ICEM CFD as shown below. Similar checks is possible in any other software such as ANSA, ANSYS Meshing, Pointwise and GridPro.
Mouse Button Setting:
The concept of Feature Area, which is defined according to the feature angle, is widely used in many functions in ANSA. The Feature Area is defined as the area of shell elements between whom the angle that is formed at their common edge is < the given feature angle. This is equivalent to "fill up to an angle" in ICEM CFD. Similarly for edges "Feature Line" selection tool uses the concept of "Corner Angle" which is defined as the angle formed by two consecutive element edges.ANSA Geometry Check Options:
SETs: for management of SET groups of ANSA entities like elements, properties, Faces, ... The CONS (Curves ON Surfaces) are the boundaries of the Faces. According to their connectivity, they are colored in Red (single edge), Yellow (double connectivity), Cyan (triple of more connectivity), orange when a double CONS has been joined. The Hot Points are the end points of CONS. A more handy way to deal with Faces is to use the Crosshatches. These appear as green dashed lines and represent the isoparametrics of the Surface on which the Face lays. A Face can be selected by its Crosshatch. In case that a Face is “frozen” (by the Freeze function), its crosshatch is colored in blue.
Use the function CHECK > GEOMETRY to identify and fix automatically some problems. Watertight preparation: Having extracted the outer surfaces, you must create the watertight model by sealing all gaps and eliminating the overlaps. If these gaps are small (close to the Tolerances), they can be closed by TOPO or PASTE functions. If they exceed (by far) the tolerances, then new Faces must be created (usually with SURFs>COONS) to close them.
Checking for intersections and proximities at Geometry level: You should make some checks for intersection and proximity while constructing your model. First of all, use the CHECKs > PENETRATION [Intersections] to locate intersecting areas (wrong topology, misplaced parts etc). Fix these areas using TOPO functions (like FACEs>INTERSECT). Use the ISOLATE > FLANGES [Proximity] function to isolate Faces within a certain distance apart. This will indicate you all the proximity problem areas that may cause problems in volume meshing. Then use the FACEs>FUSE function to close these narrow proximity passages, where possible.ANSA Meshing Parameters Setting:
Before switching to MESH, activate SHADOW and FOCUS>UNCHECKED. If ANSA leaves any Faces visible, it means that they cannot be shaded and you should fix them also.ANSA Volume Meshing Parameters Setting:
ANSA Mesh Quality Checks:
STAR-CCM+ Volume Mesh Import:
STAR-CCM+ 3D to 2D Mesh Conversion:
/BATCH /PREP7 /COM NODE DEFINITIONS
N,10,2.3,-1.7,-13.75 N,11,1.7,-3.0,-13.75 N,12,0.0,2.3,-13.75 N,13,0.5,1.6,-13.75 N,14,1.0,1.0,-13.75
/COM Material properties EX, 1, 2.068000E+08 NUXY, 1, 2.900000E-01 DENS, 1, 7.820000E-06 GXY, 1, 8.015504E+07 ALPX, 1, 1.170000E-05 KXX, 1, 4.500000E+04
R,1,,,,,, ET, 1, 45, 0, 0, 0, 0, 0, 0 TYPE, 1 $ REAL, 1 $ MAT, 1 ESYS, 0
EN,10,29,31,53,45,30,32,54,46 EN,11,20,24,23,19,45,53,51,43 EN,12,45,53,51,43,46,54,52,44 EN,13,19,23,22,21,43,51,49,47 EN,14,43,51,49,47,44,52,50,48 EN,15,21,22,9,8,47,49,27,25
CSYS,0 /SOLUTION ANTYPE,0 /COM NODAL DISPLACEMENT RESTRAINTS D,1850,UX,0.,,,,UY,UZ,ROTX,ROTY,ROTZ /COM FACE PRESSURE LOADS SFCUM,PRES,ADD,1,1 ... SFE, 1496, 1, PRES, 0, 1.00000 SFE, 1497, 1, PRES, 0, 1.00000 SFE, 1498, 1, PRES, 0, 1.00000 SFE, 1499, 1, PRES, 0, 1.00000 ... KBC,0 TIME, 1.0000 AUTOTS,OFF NSUBST, 1 ... OUTPR,NSOL ,1 OUTPR,RSOL ,1 OUTPR,ESOL ,1 OUTPR,NLOAD ,1 OUTPR,VENG ,1 ... SOLVE FINISH
Example of mesh for a square block
(10 (zone-id first-index last-index type ND)( x1 y1 z1 x2 y2 z2 . . xn yn zn ))If 'zone-id' = 0, it provides the total number of nodes in the grid. In such a case: 'first-index' = 1, 'last-index' = total number of nodes in hexadecimal, 'type' is meaningless, 'ND' = dimensionality of the grid. There will be no X-, Y-, Z-coordinates following the statement and the parentheses for the coordinates will be omitted. For example, (10 (0 1 2bd 99 2)). Note hexadecimal system has base value of 16 (analogous to base value of 10 in decimal system) and digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. In decimal systems 358 = 3x10x10 + 5x10 + 8. In hexadecimal system, 2bd = 2x16x16 + 11x16 + 13 = 701.In MS-Excel HEX2DEC function can be used to convert a hexadecimal number into any other base. e.g. HEX2DEC("2bd") = 701. Note, hexadecimal number is represented as string even though it represents a number, due to presence of text character.
(0 "Grid:") (0 "Dimensions:") (2 2) (12 (0 1 3 0) ) (13 (0 1 a 0) ) (10 (0 1 8 0 2) ) (12 (7 1 3 1 3) ) (13 (2 1 2 2 2) ( 1 2 1 2 3 4 2 3)) (13 (3 3 5 3 2) ( 5 1 1 0 1 3 2 0 3 6 3 0)) (13 (4 6 8 3 2) ( 7 4 3 0 4 2 2 0 2 8 1 0)) (13 (5 9 9 a 2) ( 8 5 1 0)) (13 (6 a a 24 2)( 6 7 3 0)) (10 (1 1 8 1 2) ( 1.0000e+00 0.0000e+00 1.0000e+00 1.0000e+00 2.0000e+00 0.0000e+00 2.0000e+00 1.0000e+00 0.0000e+00 0.0000e+00 3.0000e+00 0.0000e+00 3.0000e+00 1.0000e+00 0.0000e+00 1.0000e+00))
Definition of zones: cell and face zones
(0 "Zone Sections") (39 (11 fluid FLUID)()) (39 (12 interior int_GEOM)()) (39 (13 interface INTERFACE_A1)()) (39 (14 interface INTERFACE_A2)()) (39 (15 velocity-inlet INLET)()) (39 (16 wall WALL_BLWR_CASING)()) (39 (17 outlet-vent OUTLET)())
solid part0 facet normal n1 n2 n3 outer loop vertex x1 y1 z1 vertex x2 y2 z2 vertex x3 y3 z3 endloop endfacet facet normal ... ... endsolid part0 solid part1 ...
The content on CFDyna.com is being constantly refined and improvised with on-the-job experience, testing, and training. Examples might be simplified to improve insight into the physics and basic understanding. Linked pages, articles, references, and examples are constantly reviewed to reduce errors, but we cannot warrant full correctness of all content.