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docs:classes:fieldsymmetry

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====== FieldSymmetry ====== The FieldSymmetry class represents the symmetry group of FlowFields. Specifically, the periodic in x,z and polynomial in y expansions inherent in FlowFields allow the follow symmetries <latex> $ \begin{align*} [u,v,w](x,y,z) &\rightarrow [-u,-v,-w](x,y,z) \\ [u,v,w](x,y,z) &\rightarrow [-u, v, w](-x,y,z) \\ [u,v,w](x,y,z) &\rightarrow [ u, -v, w](x,-y,z) \\ [u,v,w](x,y,z) &\rightarrow [ u, v, -w](x, y,-z) \\ [u,v,w](x,y,z) &\rightarrow [ u, v, w](x+\ell_x, y, z+\ell_z) \end{align*} $ </latex> Let G be the group generated by these symmetries. Specific choice of boundary conditions at the walls might constrain the symmetry group of a specific flow to a subgroup G. But for generality,the FieldSymmetry class can represent any symmetry in G. Any element of G is of the form

docs/classes/fieldsymmetry.1233676635.txt.gz · Last modified: 2009/02/03 07:57 by gibson