| 17 |
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| 18 |
The finite volume method is used to discretize the equations in |
The finite volume method is used to discretize the equations in |
| 19 |
space. The expression ``finite volume'' actually has two meanings; one |
space. The expression ``finite volume'' actually has two meanings; one |
| 20 |
is the method of cut or instecting boundaries (shaved or lopped cells |
is the method of embedded or intersecting boundaries (shaved or lopped |
| 21 |
in our terminology) and the other is non-linear interpolation methods |
cells in our terminology) and the other is non-linear interpolation |
| 22 |
that can deal with non-smooth solutions such as shocks (i.e. flux |
methods that can deal with non-smooth solutions such as shocks |
| 23 |
limiters for advection). Both make use of the integral form of the |
(i.e. flux limiters for advection). Both make use of the integral form |
| 24 |
conservation laws to which the {\it weak solution} is a solution on |
of the conservation laws to which the {\it weak solution} is a |
| 25 |
each finite volume of (sub-domain). The weak solution can be |
solution on each finite volume of (sub-domain). The weak solution can |
| 26 |
constructed outof piece-wise constant elements or be |
be constructed out of piece-wise constant elements or be |
| 27 |
differentiable. The differentiable equations can not be satisfied by |
differentiable. The differentiable equations can not be satisfied by |
| 28 |
piece-wise constant functions. |
piece-wise constant functions. |
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| 116 |
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| 117 |
\subsection{Horizontal grid} |
\subsection{Horizontal grid} |
| 118 |
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\label{sec:spatial_discrete_horizontal_grid} |
| 119 |
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| 120 |
\begin{figure} |
\begin{figure} |
| 121 |
\begin{center} |
\begin{center} |
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