docs:utils:randomfield
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docs:utils:randomfield [2009/04/01 08:27] gibson |
docs:utils:randomfield [2010/02/02 07:55] (current) |
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| <fieldname> (trailing arg 1) output file | <fieldname> (trailing arg 1) output file | ||
| </code> | </code> | ||
| - | |||
| ===== mathematics ===== | ===== mathematics ===== | ||
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| <latex> | <latex> | ||
| - | {\bf u}(x,y,z) = sum_{jklm} u_{jklm} T_l(y) exp(2 pi i (jx/Lx + kz/Lz)) {\bf e}_m | + | {\bf u}(x,y,z) = \sum_{jklm} u_{jklm} T_l(y) e^{2 \pi \, i (jx/Lx + kz/Lz)} {\bf e}_m |
| </latex> | </latex> | ||
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| <latex> | <latex> | ||
| - | u_{jklm} = (\text{random # in }[-1, 1]) * \text{smoothness}^{|l| + |j| + |k|} | + | u_{jklm} = (\text{random # in }[-1, 1]) * \text{(1-smoothness)}^{|l| + |j| + |k|} |
| </latex> | </latex> | ||
| with corrections to meet boundary and divergence conditions and rescaling so that L2Norm(u) = magnitude. | with corrections to meet boundary and divergence conditions and rescaling so that L2Norm(u) = magnitude. | ||
| + | |||
| + | The form of spectral decay chosen is crude, but normally what is needed in a random field is that | ||
| + | it meets the BCs and zero-div, is controllably smooth, and excites modes with all symmetries. It would probably be better to work the length scales Lx,Ly,Lz into the exponent of ''(1-smoothness)'', so that the variations in the random field are roughly spatially isotropic. | ||
docs/utils/randomfield.1238599641.txt.gz ยท Last modified: 2009/04/01 08:27 by gibson
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