# Title: Fluids of different densities # # Description: # # Same test as before but with a density ratio of 10. The dynamic # viscosities are identical. # # Table \ref{convergence} shows the convergence of various # solvers as a function of resolution: Gerris, the marker technique of # \cite{popinet99} and Surfer \cite{gueyffier98}. # # 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} & 0.001155 \\ # Markers & 0.3593 & 0.1397 & 0.0566 & 0.0264 & 0.0148 \\ # Surfer & - & - & 0.1233 & 0.0300 & 0.0254 \\ \hline # \end{tabular} # \end{center} # \end{table} # # \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 density.gfs # Version: 1.1.0 # Required files: convergence.ref prosperetti # Generated files: convergence.tex amplitude.eps # 3 5 GfsSimulation GfsBox GfsGEdge {} { Time { end = 1.66481717925811447992 } ApproxProjectionParams { tolerance = 1e-6 } ProjectionParams { tolerance = 1e-6 } 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 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*15.016663878457,$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