# Diff of /trunk/doc/user/levelset.tex

revision 2334 by lgraham, Mon Jan 5 04:29:06 2009 UTC revision 2335 by jfenwick, Thu Mar 26 04:33:44 2009 UTC
# Line 24  There is a technique to overcome these l Line 24  There is a technique to overcome these l
24  %  %
25  \begin{figure}  \begin{figure}
26  \center  \center
27  \scalebox{0.8}{\includegraphics{figures/unitcircle.eps}}  \scalebox{0.8}{\includegraphics{figures/unitcircle}}
28  \caption{Implicit representation of the curve $x^2 + y^2 = 1$.}  \caption{Implicit representation of the curve $x^2 + y^2 = 1$.}
29  \label{UNITCIRCLE}  \label{UNITCIRCLE}
30  \end{figure}  \end{figure}
# Line 212  The accuracy of $\phi$ is only needed wi Line 212  The accuracy of $\phi$ is only needed wi
212  %  %
213  \begin{figure}  \begin{figure}
214  \center  \center
215  \scalebox{0.5}{\includegraphics{figures/LevelSetFlowChart.eps}}  \scalebox{0.5}{\includegraphics{figures/LevelSetFlowChart}}
216  \caption{Flow chart of Level Set Method procedure \cite{LIN2005}.}  \caption{Flow chart of Level Set Method procedure \cite{LIN2005}.}
217  \label{LEVELSET FLOWCHART}  \label{LEVELSET FLOWCHART}
218  \end{figure}  \end{figure}
# Line 247  where $\Delta \rho$ is the difference in Line 247  where $\Delta \rho$ is the difference in
247  %  %
248  \begin{figure}  \begin{figure}
249  \center  \center
250  \scalebox{0.7}{\includegraphics{figures/RT2Dsetup.eps}}  \scalebox{0.7}{\includegraphics{figures/RT2Dsetup}}
251  \caption{Parameters, initial interface and boundary conditions for the Rayleigh-Taylor instability problem. The interface is defined as $\phi=0.02cos(\frac{\pi x}{\lambda}) + 0.2$. The fluids have been assigned different densities and equal viscosity (isoviscous) \cite{BOURGOUIN2006}.}  \caption{Parameters, initial interface and boundary conditions for the Rayleigh-Taylor instability problem. The interface is defined as $\phi=0.02cos(\frac{\pi x}{\lambda}) + 0.2$. The fluids have been assigned different densities and equal viscosity (isoviscous) \cite{BOURGOUIN2006}.}
252  \label{RT2DSETUP}  \label{RT2DSETUP}
253  \end{figure}  \end{figure}
# Line 367  In the visIt main window, vtk/vtu files Line 367  In the visIt main window, vtk/vtu files
367  The simulation output is shown in Figures \ref{RT2D OUTPUT1} and \ref{RT2D OUTPUT1} showing the progression of the interface of the two fluids. A diapir can be seen rising on the left-hand side of the domain, and then later on, a second one rises on the right-hand side.  The simulation output is shown in Figures \ref{RT2D OUTPUT1} and \ref{RT2D OUTPUT1} showing the progression of the interface of the two fluids. A diapir can be seen rising on the left-hand side of the domain, and then later on, a second one rises on the right-hand side.
368  \begin{figure}  \begin{figure}
369  \center  \center
370  \subfigure[t=300]{\label{RT OUTPUT300}\includegraphics[scale=0.252]{figures/RT2D200by200t300.eps}}  \subfigure[t=300]{\label{RT OUTPUT300}\includegraphics[scale=0.252]{figures/RT2D200by200t300}}
371  \subfigure[t=600]{\label{RT OUTPUT600}\includegraphics[scale=0.252]{figures/RT2D200by200t600.eps}}  \subfigure[t=600]{\label{RT OUTPUT600}\includegraphics[scale=0.252]{figures/RT2D200by200t600}}
372  \subfigure[t=900]{\label{RT OUTPUT900}\includegraphics[scale=0.252]{figures/RT2D200by200t900.eps}}  \subfigure[t=900]{\label{RT OUTPUT900}\includegraphics[scale=0.252]{figures/RT2D200by200t900}}
373  \subfigure[t=1200]{\label{RT OUTPUT1200}\includegraphics[scale=0.252]{figures/RT2D200by200t1200.eps}}  \subfigure[t=1200]{\label{RT OUTPUT1200}\includegraphics[scale=0.252]{figures/RT2D200by200t1200}}
374  \caption{Simulation output of Rayleigh-Taylor instability, showing the movement of the interface of the fluids. The contour line represents the interface between the two fluids; the zero contour of the Level Set function. Velocity vectors are displayed showing the flow field. Computational mesh used was 200$\times$200 elements.}  \caption{Simulation output of Rayleigh-Taylor instability, showing the movement of the interface of the fluids. The contour line represents the interface between the two fluids; the zero contour of the Level Set function. Velocity vectors are displayed showing the flow field. Computational mesh used was 200$\times$200 elements.}
375  \label{RT2D OUTPUT1}  \label{RT2D OUTPUT1}
376  \end{figure}  \end{figure}
377  %  %
378  \begin{figure}  \begin{figure}
379  \center  \center
380  \subfigure[t=1500]{\label{RT OUTPUT1500}\includegraphics[scale=0.252]{figures/RT2D200by200t1500.eps}}  \subfigure[t=1500]{\label{RT OUTPUT1500}\includegraphics[scale=0.252]{figures/RT2D200by200t1500}}
381  \subfigure[t=1800]{\label{RT OUTPUT1800}\includegraphics[scale=0.252]{figures/RT2D200by200t1800.eps}}  \subfigure[t=1800]{\label{RT OUTPUT1800}\includegraphics[scale=0.252]{figures/RT2D200by200t1800}}
382  \caption{Simulation output of Rayleigh-Taylor instability.}  \caption{Simulation output of Rayleigh-Taylor instability.}
383  \label{RT2D OUTPUT2}  \label{RT2D OUTPUT2}
384  \end{figure}  \end{figure}

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