docs:math:symmetry
Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
|
docs:math:symmetry [2014/12/04 11:46] gibson |
docs:math:symmetry [2014/12/04 11:53] (current) gibson [Symmetry of flows in channel geometries] |
||
|---|---|---|---|
| Line 4: | Line 4: | ||
| \begin{eqnarray*} | \begin{eqnarray*} | ||
| - | [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, 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) | + | [ u,v,w ](x,y,z) & \rightarrow [ u, v, w](x+\ell_x, y, z+\ell_z) |
| \end{eqnarray*} | \end{eqnarray*} | ||
| "Channel geometry" means a domain that is periodic or infinite in //x// and //z// | "Channel geometry" means a domain that is periodic or infinite in //x// and //z// | ||
| - | and bounded in //y//, with //-L_y/2 <= y <= L_y/2// and Dirichlet or Neumann | + | and bounded in //y//, with $-L_y/2 \leq y \leq L_y/2$ and Dirichlet or Neumann |
| boundary conditions at the bounds in //y//. The symmetry groups of velocity | boundary conditions at the bounds in //y//. The symmetry groups of velocity | ||
| fields for specific flows, with constraints such as incompressibility | fields for specific flows, with constraints such as incompressibility | ||
docs/math/symmetry.1417722375.txt.gz · Last modified: 2014/12/04 11:46 by gibson
Page Tools
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 3.0 Unported
