Meshing
Meshing
Meshing
Outline
Why is a grid needed? Element types. Grid types. Grid design guidelines. Geometry. Solution adaption. Grid import.
Geometry
The starting point for all problems is a geometry. The geometry describes the shape of the problem to be analyzed. Can consist of volumes, faces (surfaces), edges (curves) and vertices (points).
Geometry can be very simple... or more complex
Geometry creation
Geometries can be created top-down or bottom-up. Top-down refers to an approach where the computational domain is created by performing logical operations on primitive shapes such as cylinders, bricks, and spheres. Bottom-up refers to an approach where one first creates vertices (points), connects those to form edges (lines), connects the edges to create faces, and combines the faces to create volumes. Geometries can be created using the same pre-processor software that is used to create the grid, or created using other programs (e.g. CAD, graphics).
3D:
tetrahedron (tet)
prism with quadrilateral base (hexahedron or hex) prism with triangular base (wedge)
pyramid
arbitrary polyhedron
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Terminology
Cell = control volume into which domain is broken up. Node = grid point. Cell center = center of a cell. Edge = boundary of a face. Face = boundary of a cell. Zone = grouping of nodes, faces, and cells:
Wall boundary zone. Fluid cell zone.
cell center node
node edge
3D computational grid
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Logical representation.
Source: www.cfdreview.com
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This structure gives full control of the mesh grading, using edge meshing, with high-quality elements. Manual creation of multi-block structures is usually more timeconsuming compared to unstructured meshes.
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Unstructured Grid
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Quad: Submap.
Quad: Tri-Primitive.
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non-conformal interface
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Tetrahedral mesh
Start from 3D boundary mesh containing only triangular faces. Generate mesh consisting of tetrahedra.
Complex Geometries
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Surface mesh for a grid containing hexahedra, pyramids, and tetrahedra (and prisms)
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Nonconformal mesh
Parametric study of complex geometries. Nonconformal capability allows you to replace portion of mesh being changed. Start from 3D boundary mesh or volume mesh. Add or replace certain parts of mesh. Remesh volume if necessary.
nonconformal interface
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Polyhedral mesh: consists of arbitrary polyhedra. Nonconformal mesh: mesh in which grid nodes do not match up along an interface.
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Initial mesh
Boundary refinement
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Mesh quality
For the same cell count, hexahedral meshes will give more accurate solutions, especially if the grid lines are aligned with the flow. The mesh density should be high enough to capture all relevant flow features. The mesh adjacent to the wall should be fine enough to resolve the boundary layer flow. In boundary layers, quad, hex, and prism/wedge cells are preferred over tris, tets, or pyramids. Three measures of quality:
Skewness. Smoothness (change in size). Aspect ratio.
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max 90 90 min
90 , 90
max
min
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Equiangle skewness
Common measure of quality is based on equiangle skew. Definition of equiangle skew:
max e e min max , 180 e e
where:
max = largest angle in face or cell. min = smallest angle in face or cell. e = angle for equiangular face or cell.
e.g., 60 for triangle, 90 for square.
max min
Range of skewness:
0 best 1 worst
Aspect ratio is ratio of longest edge length to shortest edge length. Equal to 1 (ideal) for an equilateral triangle or a square.
aspect ratio = 1
high-aspect-ratio quad
aspect ratio = 1
high-aspect-ratio triangle
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If such violations exist: delete mesh, perform necessary decomposition and/or pre-mesh edges and faces, and remesh.
Value of Skewness Cell Quality 0-0.25 excellent 0.25-0.50 good 0.50-0.80 acceptable 0.80-0.95 0.95-0.99 poor sliver 0.99-1.00 degenerate
flow
inadequate
better
Cell aspect ratio (width/height) should be near one where flow is multi-dimensional. Quad/hex cells can be stretched where flow is fully-developed and essentially one-dimensional.
Flow Direction
OK!
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xi
xi+1
x i+1 1 .2 x i
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Solution adaption
How do you ensure adequate grid resolution, when you dont necessarily know the flow features? Solution-based grid adaption! The grid can be refined or coarsened by the solver based on the developing flow:
Solution values. Gradients. Along a boundary. Inside a certain region.
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Grid adaption
Grid adaption adds more cells where needed to resolve the flow field. Fluent adapts on cells listed in register. Registers can be defined based on:
Gradients of flow or user-defined variables. Isovalues of flow or user-defined variables. All cells on a boundary. All cells in a region. Cell volumes or volume changes. y+ in cells adjacent to walls. Combine adaption registers. Draw contours of adaption function. Display cells marked for adaption. Limit adaption based on cell size and number of cells.
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Summary
Design and construction of a quality grid is crucial to the success of the CFD analysis. Appropriate choice of grid type depends on:
Geometric complexity. Flow field. Cell and element types supported by solver.
Hybrid meshing offers the greatest flexibility. Take advantage of solution adaption.
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