computational fluid dynamics cfd - lunds tekniska högskola
TRANSCRIPT
Computational Fluid Dynamics
CFD
Solving system of equations,
Grid generation
2
Basic steps of CFD
Problem
?
•Gov. Eq.
•BC
•Init. Cond.
...,, jijti uu
•Discretization •Result
•Solution•OK?
Discretisation and grid
Questions:
•How complex is the geometry?
•What accuracy is required? Grid quality?
•What about stability?
•Grid refinement?
Grid generation-classification
4
Structured
Number of blocks
Mono Multi
Hierarchy
Cartesian
Shape
H C O
Orthogonality
Orthogonal
Body-fitted
Oct-tree
Unstructured
Tetra-hedral
Poly-hedral
Cell types
2-dimensional 3-dimensional
Triangular
(tri)
Quadrilateral
(quad)
Tetrahedron
(tet)
Hexahedron
(hex)
pyramid wedge
Grid types
Structured grid Unstructured grid
Unstructured grid
Grid types
Structured grid
Multi-block
Grid types
Hybrid grid
Grid typesHybrid grid
10
Structured
• Easy to generate
• Inbuilt topology
• Low memory footprint
• Fast solution algorythms
• Easy to use high-order schemes
• Difficult for complex geometries
Unstructured
• Difficult to generate
• Topology has to be stored
• Lower mesh quality
• Slow algorythms
• Difficult for high-order
• Suitable for complex geometries
Mesh quality measures
11
• Stretching
• dy2/dy1
• Best: 1
• Aspect ratio
• dy1/dx
• Best: 1
• Skewness
a
• Best: equi-angle
a
dx
dy1
dy2
Efficient grids – grid stretching
12
Large gradients
Fine resolution
Efficient grids – grid stretching
13
i
i+1
i-1
...62 3
33
2
22
1
iii
iix
Tx
x
Tx
x
TxTT
...6
)(
2
)(3
33
2
22
1
iii
iix
Txr
x
Txr
x
TxrTT
)(2
)1(
)1(
2
2
2
11 xOx
Txr
xr
TT
x
T
i
ii
• Not second order any
more!
• Can be corrected
• Extra work
Grid stretching
Grid stretching
Efficient grids – local refinement
16
Efficient grids – adaptive
refinement
17
• Right marker parameter
• P, u, T, dt/dx, etc.
• Not too often
• Comp. Time
• Errors introduced
• Not too late
• Follow the flow
features
Refinement techniques
18
• Easier to implement
• Mesh quality
decreases
• Neighbours affected
• Better quality
Other grid related issues
• Grid generation strategies
• Moving boundaries