docs:utils:findsoln
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| ====== findsoln ====== | ====== findsoln ====== | ||
| - | find an equilibrium, traveling wave, periodic orbit, or relative periodic orbit of plane Couette or channel flow | + | find an equilibrium, traveling wave, periodic orbit, or relative periodic orbit of plane Couette or channel flow, |
| + | using a [[docs:math:newton_krylov_hookstep| Newton-Krylov-hookstep search algorithm]]. | ||
| ====== main options ====== | ====== main options ====== | ||
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| </code> | </code> | ||
| + | ====== 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 several kinds of solutions | ||
| + | |||
| + | * equilibrium: //σ = 1///, all //T// | ||
| + | * 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) | ||
| + | * 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) | ||
| + | |||
| + | 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^ | ||
| + | |''findsoln -eqb uguess.h5'' | equilibrium solution | | ||
| + | |''findsoln -eqb -xrel uguess.h5'' | traveling wave in //x// | | ||
| + | |''findsoln -eqb -xrel -zrel uguess.h5'' | traveling wave in //x,z// | | ||
| + | |''findsoln -eqb -zrel -sigma sigma.asc -T 20 uguess.h5'' | traveling wave in //z// with an initial guess for wavespeed | | ||
| + | |''findsoln -orb -T 64.3 uguess.asc'' | periodic orbit with initial guess for period //T// | | ||
| + | |''findsoln -orb -T 34.8 -sigma sigma.asc uguess.h5'' | pre-periodic orbit | | ||
| + | |''findsoln -orb -xrel -T 49.1 -sigma sigma.asc uguess.h5'' | relative periodic orbit with phase shift in //x// | | ||
| + | |||
| + | |||
| + | ([[docs:math:newton_krylov_hookstep|mathematical details of algorithm]] | ||
docs/utils/findsoln.1267717942.txt.gz · Last modified: 2010/03/04 07:52 by gibson
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