# Title: Planar capillary waves
#
# Description:
#
# A small amplitude sinusoidal wave oscillates under surface
# tension. Prosperetti \cite{prosperetti81} found a solution to this
# initial value problem in the limit of a vanishingly small initial
# amplitude.
#
# The domain size is 1x3 units, large enough to minimise the effect of
# boundaries (Prosperetti's theory is valid for infinite domains).
#
# Table \ref{convergence} shows the convergence of various solvers as
# a function of resolution: Gerris, the marker technique of
# \cite{popinet99}, Surfer \cite{gueyffier98}, PROST and CLSVOF
# \cite{gerlach2006}. The same data is represented on Figure \ref{fig-convergence}.
#
# The time-evolution of the amplitude given by Prosperetti's theory
# and Gerris ($64^2$) is given on Figure \ref{amplitude}.
#
# \begin{table}[htbp]
# \caption{\label{convergence}Convergence of the relative error between the analytical
# solution and simulation results from various solvers.}
# \begin{center}
# \begin{tabular}{|l|ccccc|} \hline
# Method & $8^2$ & $16^2$ & $32^2$ & $64^2$ & $128^2$ \\ \hline
# \input{convergence.tex} & 0.000545 \\
# \input{markers.tex} \\
# \input{surfer.tex} \\
# \input{prost.tex} \\
# \input{clsvof.tex} \\ \hline
# \end{tabular}
# \end{center}
# \end{table}
#
# \begin{figure}[htbp]
# \caption{\label{fig-convergence}Convergence of the RMS error as a
# function of resolution (number of grid points per wavelength) for
# the methods indicated in the legend.}
# \begin{center}
# \includegraphics[width=\hsize]{convergence.eps}
# \end{center}
# \end{figure}
#
# \begin{figure}[htbp]
# \caption{\label{amplitude}Evolution of the amplitude of the capillary wave as a
# function of non-dimensional time $\tau=\omega_0 t$.}
# \begin{center}
# \includegraphics[width=\hsize]{amplitude.eps}
# \end{center}
# \end{figure}
#
# Author: St\'ephane Popinet
# Command: sh capwave.sh capwave.gfs
# Version: 1.1.0
# Required files: capwave.sh convergence.ref prosperetti markers.tex surfer.tex prost.tex clsvof.tex
# Generated files: convergence.tex amplitude.eps convergence.eps markers.tex surfer.tex prost.tex clsvof.tex
#
3 5 GfsSimulation GfsBox GfsGEdge {} {
  Time { end = 2.2426211256 }
  ApproxProjectionParams { tolerance = 1e-6 }
  ProjectionParams { tolerance = 1e-6 }
  # Decrease the resolution linearly down to 3 levels close to the
  # bottom and top boundaries
  Refine floor(LEVEL + 1 - (LEVEL - 2)*fabs(y)/1.5)
  VariableTracerVOF T
  VariableCurvature K T
  SourceTension T 1 K
  VariablePosition Y T y
  SourceDiffusion U 0.0182571749236
  SourceDiffusion V 0.0182571749236
  InitFraction T (y - 0.01*cos (2.*M_PI*x))
  OutputScalarNorm { step = 3.04290519077e-3 } {
      awk '{printf ("%g %g\n", $3*11.1366559937, $9); fflush(stdout); }' > wave-LEVEL
  } { v = (T > 0. && T < 1. ? Y : 0.) }
}
GfsBox {}
GfsBox {}
GfsBox {}
1 1 right
2 2 right
3 3 right
1 2 top
1 3 bottom