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TRANSFORMATION OF
GRID(MESH)Presented by:- Submitted to:-SAURAV SUMAN Dr. VARUN
Department of Mechanical EngineeringNATIONAL INSTITUTE OF TECHNOLOGY,HAMIRPUR
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CONTENT:- Introduction
Types of meshes(grids) Grid generation process
o Conformal mapping
o
Algebraic mappingo PDE methods
Grid generation technique
Structured meshing
Unstructured meshing
o Advance fronting method
o Quadtree method11/25/12 22
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INTRODUCTION
Why we mesh any product?
CAD(continuous Model)
Mesh(discrete Model)11/25/12 33
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Type of mesh (Element type)
2-Dimensional
Triangles, Quadrilateral
3-Dimensional
Tetrahedral, Hexahedral, Prism, pyramid
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Types of mesh (Arrangement)
Structured (Regular)- Interior nodes attached to same number of elements.
- Several Techniques can be used to map a computational domain into aphysical domain: Transfinite Interpolation, Morphing, PDE Based etc.
Unstructured (Irregular)- Interior nodes attached to variable number of elements.
- Three main techniques are available to generate automatically triangle(tetrahedra): Delaunay triangulation, Advancing front, Octree.
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Grid generation process Grid generation is the process of determining the coordinate transformation
that maps the body-fitted non-uniform non-orthogonal physical spacex,y,z,t into the transformed uniform orthogonal computational space,,,.
Types of grid generation process:-
1.
Conformal Mapping: based on complex variable theory, which islimited to two dimensions.
2. Algebraic methods:
i. 1D: polynomials, trigonometric functions, logarithmic functions.
ii. 2D: Orthogonal one-dimensional transformation, connectionfunctions.
1. Differential equation methods:
Step 1: Determine the grid point distribution on the boundaries of thephysical space.
Step 2: Assume the interior grid point is specified by a differential11/25/12 66
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Conformal Mapping Any function = f(z) such that, 0 defines a one-to-one (conformal)
mapping between z = x+iy and =+i, or between (x,y) and (,).
Lead to high quality grids, preserve ratios.
Limited to 2D.
Some of conformal mapping transformations as Jukoswki, Schwaz-
Cristoffel mapping etc.
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Algebraic Mapping Construct a mapping between the boundaries of the unit square (cube)
and the boundaries of an arbitrary region which is topologicallyequivalent.
Combine 1D interpolants using boolean sums to construct mapping Transfinite Interpolation (TFI).
Very fast
Quite General
Not guaranteed to one-by-one
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Differential equation method Construct mapping by solving a PDE
Elliptic equations (smooth grids)
Hyperbolic equations (orthogonal grids)
Most widely used approach
Grids usually have high quality
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Grid generation techniques
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Structured meshing Construct a one-to-one mapping between a rectangular
computational domain and a physical domain
O-grid C-grid
H-grid11/25/12 1111
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Unstructured meshing
Advance fronting method
- Place nodes around boundary
- Loop through all edges on front
- Create triangle, check radius around optimal nodes for front
- If choice between multiple nodes, chose best quality element,continue until finish
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Quadtree (Octree) method Build quadtree to resolve geometry
Add nodes to intersection of 2 quadtree lines and boundry toquadtree line
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Mesh structure using nodes with triangles
Final mesh
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Delaunay triangulation
No other vertex is contained within the circumcircle of any triangle
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Delaunay-Interior nodes Begin with bounding triangles
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Grid based nodes introduced based on a regular lattice
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Hybrid mesh Hybrid meshes contain
Structured/Cartesian Parts
Unstructured Parts
Hybrid meshes are often used in CFD, especially for boundarylayer meshes
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THANK YOU
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