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Computational Fluid Dynamics
Lecture 25
{}
1
J
x
yz
x
x
ξη
ζ
η
ξ
=
−−
−+
−
The metrics can be readily determined if analytical expressions are available for the inverse of the
transformation.
()
,,
xx
yy
zz
ξηζ
=
=
=
For cases where the transformation is the result of a grid generation scheme, the metrics are
computed numerically using central differences.
The problem of grid generation is determining the mapping between the physical domain and the
computational domain.
Desired Features:
1. One to one mapping.
2. Grid lines should be smooth.
3. Grid points should be closely spaced in physical space where large numerical errors are
expected.
4. Excessive grid skewness should be avoided.
Grid generation in one dimension is simple, many functions can generate satisfactory grids.
There are three basic techniques for 2D grid generation.
1. Complex variable techniques.
2. Algebraic methods.
3. Differential equation techniques
Complex variable techniques are analytic, as opposed to numerical methods.
Disadvantage is restricted to 2D, no 3D extension.
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 Spring '07
 Slinn

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