# Title: Axisymmetric spherical droplet in equilibrium
#
# Description:
#
# The same test case but using the axisymmetric solver. The results
# are comparable.
#
# \begin{figure}[htbp]
# \caption{\label{laplace}Evolution of the amplitude of the capillary currents
# $\max(|{\bf u}|)(D/\sigma)^{1/2}$ as a function of
# non-dimensional time $\tau=t\mu/D^2$ for the range of Laplace
# numbers indicated in the legend.}
# \begin{center}
# \includegraphics[width=0.8\hsize]{laplace.eps}
# \end{center}
# \end{figure}
#
# \begin{figure}[htbp]
# \caption{\label{curvature}Evolution of the standard deviation of the
# value of the curvature along the interface as a function of
# non-dimensional time $\tau=t\mu/D^2$ for the range of Laplace
# numbers indicated in the legend.}
# \begin{center}
# \includegraphics[width=0.8\hsize]{curvature.eps}
# \end{center}
# \end{figure}
#
# \begin{figure}[htbp]
# \caption{\label{convergence}Convergence of the error on the equilibrium shape of the
# droplet with resolution. The diameter is given in number of grid
# points.}
# \begin{center}
# \includegraphics[width=0.8\hsize]{convergence.eps}
# \end{center}
# \end{figure}
#
# \begin{figure}[htbp]
# \caption{\label{kconvergence}Convergence of the relative error on the
# equilibrium curvature value with resolution. The diameter is given
# in number of grid points.}
# \begin{center}
# \includegraphics[width=0.8\hsize]{kconvergence.eps}
# \end{center}
# \end{figure}
#
# Author: St\'ephane Popinet
# Command: sh ../spurious.sh axi.gfs 1e-7
# Version: 1.3.1
# Required files: convergence.ref kconvergence.ref
# Generated files: laplace.eps curvature.eps convergence.eps kconvergence.eps
#

Define CIRCLE (ellipse (-0.5,0.,0.4,0.4))
Define MU sqrt(0.8/LAPLACE)

1 0 GfsAxi GfsBox GfsGEdge {} {
  Time { end = TMAX }
  Refine LEVEL
  RefineSurface {return 10;} CIRCLE

  ApproxProjectionParams { tolerance = 1e-6 }
  ProjectionParams { tolerance = 1e-6 }
  AdvectionParams { scheme = none }

  VariableTracerVOF T
  VariableCurvature K T
  SourceTension T 1 K
  SourceViscosity MU

  InitFraction T CIRCLE
  Init {} { Tref = T }

  AdaptGradient { istep = 1 } { cmax = 1e-6 maxlevel = LEVEL } T
  EventStop { istep = 10 } T DT

  OutputSimulation { start = end } stdout { depth = LEVEL }
  OutputScalarNorm { istep = 1 } {
    awk '{ print MU*$3/(0.8*0.8), $9*sqrt(0.8); fflush (stdout); }' > La-LAPLACE-LEVEL
  } { v = Velocity }
  OutputScalarNorm { istep = 1 } {
    awk '{ print MU*$3/(0.8*0.8), $5, $7, $9; fflush (stdout); }' > E-LAPLACE-LEVEL
  } { v = (Tref - T) }
  OutputScalarStats { istep = 1 } {
    awk '{ print MU*$3/(0.8*0.8), $5, $7, $9, $11; fflush (stdout); }' > K-LAPLACE-LEVEL
  } { v = (K - 2.50771) }
  OutputScalarNorm { istep = 1 } {
    awk '{ print MU*$3/(0.8*0.8), $5, $7, $9; fflush (stdout); }' > EK-LAPLACE-LEVEL
  } { v = (T > 0 && T < 1 ? (K - 5.)/2. : 0) }
}
GfsBox {
  bottom = Boundary
  left = Boundary
}