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\subsection{The finite volume method: finite volumes versus finite difference} |
\subsection{The finite volume method: finite volumes versus finite difference} |
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<!-- CMIREDIR:finite_volume: --> |
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\end{rawhtml} |
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The finite volume method is used to discretize the equations in |
The finite volume method is used to discretize the equations in |
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space. The expression ``finite volume'' actually has two meanings; one |
space. The expression ``finite volume'' actually has two meanings; one |
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\end{eqnarray} |
\end{eqnarray} |
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where the continuity equation has been most naturally discretized by |
where the continuity equation has been most naturally discretized by |
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staggering the three components of velocity as shown in |
staggering the three components of velocity as shown in |
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Fig.~\ref{fig-cgrid3d}. The grid lengths $\Delta x_c$ and $\Delta y_c$ |
Fig.~\ref{fig:cgrid3d}. The grid lengths $\Delta x_c$ and $\Delta y_c$ |
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are the lengths between tracer points (cell centers). The grid lengths |
are the lengths between tracer points (cell centers). The grid lengths |
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$\Delta x_g$, $\Delta y_g$ are the grid lengths between cell |
$\Delta x_g$, $\Delta y_g$ are the grid lengths between cell |
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corners. $\Delta r_f$ and $\Delta r_c$ are the distance (in units of |
corners. $\Delta r_f$ and $\Delta r_c$ are the distance (in units of |
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