/[escript]/trunk/doc/user/levelset.tex
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revision 2881 by jfenwick, Thu Jan 28 02:03:15 2010 UTC revision 3279 by caltinay, Fri Oct 15 04:02:06 2010 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}}  \scalebox{0.8}{\includegraphics{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}}  \scalebox{0.5}{\includegraphics{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}}  \scalebox{0.7}{\includegraphics{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 384  In the visIt main window, vtk/vtu files Line 384  In the visIt main window, vtk/vtu files
384  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.
385  \begin{figure}  \begin{figure}
386  \center  \center
387  \subfigure[t=300]{\label{RT OUTPUT300}\includegraphics[scale=0.252]{figures/RT2D200by200t300}}  \subfigure[t=300]{\label{RT OUTPUT300}\includegraphics[scale=0.252]{RT2D200by200t300}}
388  \subfigure[t=600]{\label{RT OUTPUT600}\includegraphics[scale=0.252]{figures/RT2D200by200t600}}  \subfigure[t=600]{\label{RT OUTPUT600}\includegraphics[scale=0.252]{RT2D200by200t600}}
389  \subfigure[t=900]{\label{RT OUTPUT900}\includegraphics[scale=0.252]{figures/RT2D200by200t900}}  \subfigure[t=900]{\label{RT OUTPUT900}\includegraphics[scale=0.252]{RT2D200by200t900}}
390  \subfigure[t=1200]{\label{RT OUTPUT1200}\includegraphics[scale=0.252]{figures/RT2D200by200t1200}}  \subfigure[t=1200]{\label{RT OUTPUT1200}\includegraphics[scale=0.252]{RT2D200by200t1200}}
391  \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.}
392  \label{RT2D OUTPUT1}  \label{RT2D OUTPUT1}
393  \end{figure}  \end{figure}
394  %  %
395  \begin{figure}  \begin{figure}
396  \center  \center
397  \subfigure[t=1500]{\label{RT OUTPUT1500}\includegraphics[scale=0.252]{figures/RT2D200by200t1500}}  \subfigure[t=1500]{\label{RT OUTPUT1500}\includegraphics[scale=0.252]{RT2D200by200t1500}}
398  \subfigure[t=1800]{\label{RT OUTPUT1800}\includegraphics[scale=0.252]{figures/RT2D200by200t1800}}  \subfigure[t=1800]{\label{RT OUTPUT1800}\includegraphics[scale=0.252]{RT2D200by200t1800}}
399  \caption{Simulation output of Rayleigh-Taylor instability.}  \caption{Simulation output of Rayleigh-Taylor instability.}
400  \label{RT2D OUTPUT2}  \label{RT2D OUTPUT2}
401  \end{figure}  \end{figure}

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