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Mon Dec 8 02:27:07 2008 UTC (12 years, 1 month ago) by lgraham
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starting a section for the Level Set class in the Models chapter.

1 lgraham 2138 \subsection{Level Set Method}
3     \subsection{Solution Method}
5     \subsection{Functions}
7     \begin{classdesc}{LevelSet}{domain, func, reinit\_max, reinit\_each, tolerance, smooth}
8     opens the LevelSet \index{Level Set} on the \Domain domain. \var{func} defines the initial Level Set function representing the interface between two fluids. \var{reinit\_max} sets the maximum number of interations to satisfy the normal condition, $|\nabla \phi|=1$, during the reinitilization of the Level Set function. \var{reinit\_each} sets the frequency of reinitialization for a number of time-steps. \var{tolerance} sets the convergence tolerance of the error to satisfy the normal condition during the reinitilization of the Level Set function. \var{smooth} sets the bandwidth of size 2$\alpha h$ along the interface to smooth the physical parameters of density and viscosity; $h$ is the size of the elements in the mesh and $\alpha$ is the smoothing parameter, usually set to 1.
9     \end{classdesc}
11     \begin{methoddesc}[LevelSet]{update\_parameter}{par1, par2}
12     updates the physical parameters using the sign of $\phi$. \var{par1} and \var{par2} are the physical parameter values for the two different fluids, for example, the densities of the two fluids. Usually this method is called twice during each time-step to update the density and viscosity of the two fluids.
13     \end{methoddesc}
15     \begin{methoddesc}[LevelSet]{update\_phi}{vel, dt, t\_step}
16     updates the Level Set function. It performs the advection and reinitialization procedures. \var{vel} is the velocity field of the fluids, \var{dt} is the time-step size, and \var{t\_step} is the current time-step to determine when to reinitialize.
17     \end{methoddesc}
20     %\begin{methoddesc}[LevelSet]{update}{\optional{f=Data(), \optional{fixed_u_mask=Data(), \optional{eta=1, \optional{surface_stress=Data(), \optional{stress=Data()}}}}}}
22     %\begin{methoddesc}[StokesProblemCartesian]{update\_phi}{v,p,
23     %\optional{max_iter=20, \optional{verbose=False, \optional{useUzawa=True}}}}
24     %solves the problem and return approximations for velocity and pressure.
25     %The arguments \var{v} and \var{p} define initial guess. The values of \var{v} marked
26     %by \var{fixed_u_mask} remain unchanged.
27     %If \var{useUzawa} is set to \True
28     %the Uzawa\index{Uszwa} scheme is used. Otherwise the problem is solved in coupled form. In most cases
29     %the Uzawa scheme is more efficient.
30     %\var{max_iter} defines the maximum number of iteration steps.
31     %If \var{verbose} is set to \True informations on the progress of of the solver are printed.
32     %\end{methoddesc}

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