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2.3.3 Discretization in space by finite volumes

Finite volume methods:

To go from continuous values of \bgroup\color{DEFcolor}$\rho(x)$\egroup to a discrete set of values \bgroup\color{DEFcolor}$\rho_i$\egroup for a grid with \bgroup\color{DEFcolor}$x_i = \Delta x  i + x_0$\egroup we integrate over the ``control volume'' associated to each grid point. In one dimension that might be

\rho_i = \frac{1}{\Delta x} \int\limits_{x_i-\Delta x/2}^{x_i+\Delta x/2} \rho \left( x \right)   dx
\enspace .
\end{displaymath} (94)