# Title: Pure gravity wave
#
# Description:
#
# Similar to the capillary wave test case but for a pure gravity
# wave. The density ratio is 10. The dynamic viscosities are
# identical.
#
# 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.}
# \begin{center}
# \begin{tabular}{|l|ccccc|} \hline
# Method & $8^2$ & $16^2$ & $32^2$ & $64^2$ & $128^2$ \\ \hline
# \input{convergence.tex} & 0.00417707 \\
# \end{tabular}
# \end{center}
# \end{table}
#
# \begin{figure}[htbp]
# \caption{\label{amplitude}Evolution of the amplitude of the gravity 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 gravity.gfs
# Version: 1.0.0
# Required files: convergence.ref prosperetti
# Generated files: convergence.tex amplitude.eps
#
1 1 GfsSimulation GfsBox GfsGEdge {} {
  Time { end = 1.66481717925811447992 }
  ApproxProjectionParams { tolerance = 1e-6 }
  ProjectionParams { tolerance = 1e-6 }
  Refine LEVEL
  VariableTracerVOF {} T

  # Line below is for direct imposition of gravity acceleration
  #  Source {} V 50

  # It is better to use a formulation where the first-order
  # hydrostatic pressure is substracted away (in particular it
  # prevents the generation of "hydrostatic spurious currents")
  VariablePosition {} Y T y

  # acceleration of gravity is 50, the equivalent "reduced pressure"
  # is 50*(1. - 0.1) = 45
  SourceTension {} T 45 Y

  SourceDiffusion {} U 0.0182571749236
  SourceDiffusion {} V 0.0182571749236
  PhysicalParams { alpha = 1./(T + 0.1*(1. - T)) }
  InitFraction {} T (y - 0.01*cos (2.*M_PI*x))
  OutputScalarNorm { step = .00225584983639310905 } {
      awk '{printf ("%g %g\n", $3*16.032448313657, $9); fflush(stdout); }' > wave-LEVEL
  } { v = (T > 1e-6 && T < 1. - 1e-6 ? Y : 0.) }
}
GfsBox {}
1 1 right