docs:utils:findsoln
Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision Last revision Both sides next revision | ||
|
docs:utils:findsoln [2010/03/04 08:39] gibson |
docs:utils:findsoln [2010/03/04 08:48] gibson |
||
|---|---|---|---|
| Line 22: | Line 22: | ||
| ====== solution type ====== | ====== solution type ====== | ||
| - | ''findsoln'' finds solutions of //σ f^T(u) - u = 0// where //f^T// is the time-//T// forward map of the Navier-Stokes equations plus boundary conditions and σ is a symmetry of the flow. This equation has four kinds of solutions | + | ''findsoln'' finds solutions of //σ f^T(u) - u = 0// where //f^T// is the time-//T// forward map of the Navier-Stokes equations plus boundary conditions and σ is a symmetry of the flow. This equation has several kinds of solutions |
| * equilibrium: //σ = 1///, all //T// | * equilibrium: //σ = 1///, all //T// | ||
| - | * relative equilibrium: //σ = // a translation that scales linearly in //T//, all //T// (also called a traveling wave) | + | * relative equilibrium: //σ = // a translation or phase shift that scales linearly in //T//, all //T// (also called a traveling wave) |
| * periodic orbit: //σ = 1// and some finite value of //T// (and integer multiples of it) | * periodic orbit: //σ = 1// and some finite value of //T// (and integer multiples of it) | ||
| - | * preperiodic orbit: //σ ≠ 1// but //σ^n = 1// for some //n>1//, and some finite value of //T// (and integer multiples_ | + | * preperiodic orbit: //σ ≠ 1// but //σ^n = 1// for some //n>1//, and some finite value of //T// (and integer multiples) |
| * relative periodic orbit: some element //σ// of the appropriate symmetry group, and some finite value of //T// (and integer multiples) | * relative periodic orbit: some element //σ// of the appropriate symmetry group, and some finite value of //T// (and integer multiples) | ||
| - | You specify which kind of solution to find with the <code> -eqb, -orb, -xrel, -zrel</code> options. The symmetry σ for the relative equilibrium and relative periodic orbit solutions involves unknown phase shifts (translations) in //x//, //z//, or both //x,z//, depending on the symmetry of the initial guess //u//, and you specify which to treat as unknowns by using the ''-xrel'' and ''-zrel'' options. Here are some examples of searches of various types | + | You specify which kind of solution to find by telling the search algorithm which variables to treat as unknowns, with the ''-eqb, -orb, -xrel, -zrel'' options. The ''-eqb'' option specifies that //T// is held fixed; the ''-orb'' option specifies that is unknown. The ''-xrel'' and ''-zrel'' options specifying that the //x// and //z// phase shifts in σ are unknown. The appropriate combinations for each solution type are best shown by example. |
| ^command^search type^ | ^command^search type^ | ||
docs/utils/findsoln.txt · Last modified: 2010/03/04 17:37 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
