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docs:utils:couette [2009/02/13 08:45]
gibson
docs:utils:couette [2010/02/02 07:55] (current)
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 ''​couette''​ integrates plane Couette or channel flow from a given initial condition and save velocity fields to disk at a regular interval. (It should probably be called ''​integrate'';​ I might change it to that in the next release.) ''​couette''​ integrates plane Couette or channel flow from a given initial condition and save velocity fields to disk at a regular interval. (It should probably be called ''​integrate'';​ I might change it to that in the next release.)
- 
 ====== main options ====== ====== main options ======
  
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   -P        --dPdx ​             <​real> ​     default == 0           value for fixed pressure gradient   -P        --dPdx ​             <​real> ​     default == 0           value for fixed pressure gradient
   -U        --Ubulk ​            <​real> ​     default == 0           value for fixed bulk velocity   -U        --Ubulk ​            <​real> ​     default == 0           value for fixed bulk velocity
 +  -symms ​   --symmetries ​       <​string> ​   default == "" ​         filename for generators of flow-invariant symmetry subspace
   <​flowfield> ​     (trailing arg 1)                                initial condition   <​flowfield> ​     (trailing arg 1)                                initial condition
 </​code>​ </​code>​
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 |''​sbdf3''​| ​ 3  |Semi-implict Backwards Differentiation| |''​sbdf3''​| ​ 3  |Semi-implict Backwards Differentiation|
 |''​sbdf4''​| ​ 4  | Semi-implict Backwards Differentiation| |''​sbdf4''​| ​ 4  | Semi-implict Backwards Differentiation|
- 
 ===== nonlinearity ===== ===== nonlinearity =====
  
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 ^  value  ^      ^method^ ^  value  ^      ^method^
- ''​rot'' ​ |  (∇×u)×u ​ |rotational| +|''​rot''​| ​ (∇×u)×u ​ |rotational| 
- ''​conv''​ |  u⋅∇u ​  ​|convection| +|''​conv''​| ​ u⋅∇u ​ |convection| 
- ''​div'' ​ |  ∇⋅(uu) ​ |divergence| +|''​div''​| ​ ∇⋅(uu) ​ |divergence| 
-| ''​skew'' ​ |  (u⋅∇u + ∇⋅(uu))/​2 |skew-symmetric| +|''​skew''​| ​ (u⋅∇u + ∇⋅(uu))/​2 ​ |skew-symmetric| 
-| ''​alt'' ​  ​  ​|alternating between ''​conv''​ and ''​div''​|+|''​alt''​| |alternating between ''​conv''​ and ''​div''​|
  
 ===== mean constraints ===== ===== mean constraints =====
 +===== symmetries =====
  
-====== Usage examples ======+The ''​-symms filename.asc''​ option will cause the numerically integrated solution to be periodically projected onto a flow-invariant symmetric subspace specified by the named file. The file should list the generators of the subspace'​s symmetry group. For example, suppose you want to restrict integration to the symmetry group ''​S ​{s1,​s2,​s3}''​
  
 +<​latex>​
 + $ \begin{align*}
 +  s_1 \, [u, v, w](x,y,z) &= [u, v, -w](x+L_x/​2,​ y, -z) \\
 +  s_2 \, [u, v, w](x,y,z) &= [-u, -v, w](-x+L_x/​2,​-y,​z+L_z/​2) \\
 +  s_3 \, [u, v, w](x,y,z) &= [-u,​-v,​-w](-x,​ -y, -z+L_z/2) \\
 +\end{align*}
 +
 +</​latex>​
  
 +s1 and s2 are generators of S. So construct a file s1s2.asc with these contents
 +
 +  % 2
 +  1  1  1 -1  0.5  0.0
 +  1 -1 -1  1  0.5  0.5
 +
 +The first line specifies the number of generators, and the following lines specify the generators, according to
 +
 +  c sx sy sz ax az
 +
 +where 
 +
 +  (c sx sy sz ax az) [u, v, w](x, y, z) → c [sx u, sy v, sz w](sx x + ax Lx, sy y, sz z + az Lz)
 + 
 +This functionality is provided because numerical errors and instability of invariant symmetric subspaces will cause numerical solutions to drift out of the invariant subspaces. The integration routines do the project at intervals ''​dT''​.  ​
 +
 +
 +====== Usage examples ======
docs/utils/couette.1234543553.txt.gz · Last modified: 2009/02/13 08:45 by gibson