--- manual/s_algorithm/text/spatial-discrete.tex 2001/09/26 21:59:33 1.7 +++ manual/s_algorithm/text/spatial-discrete.tex 2001/10/24 15:21:27 1.9 @@ -1,4 +1,4 @@ -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_algorithm/text/spatial-discrete.tex,v 1.7 2001/09/26 21:59:33 adcroft Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_algorithm/text/spatial-discrete.tex,v 1.9 2001/10/24 15:21:27 cnh Exp $ % $Name: $ \section{Spatial discretization of the dynamical equations} @@ -17,13 +17,13 @@ The finite volume method is used to discretize the equations in space. The expression ``finite volume'' actually has two meanings; one -is the method of cut or instecting boundaries (shaved or lopped cells -in our terminology) and the other is non-linear interpolation methods -that can deal with non-smooth solutions such as shocks (i.e. flux -limiters for advection). Both make use of the integral form of the -conservation laws to which the {\it weak solution} is a solution on -each finite volume of (sub-domain). The weak solution can be -constructed outof piece-wise constant elements or be +is the method of embedded or intersecting boundaries (shaved or lopped +cells in our terminology) and the other is non-linear interpolation +methods that can deal with non-smooth solutions such as shocks +(i.e. flux limiters for advection). Both make use of the integral form +of the conservation laws to which the {\it weak solution} is a +solution on each finite volume of (sub-domain). The weak solution can +be constructed out of piece-wise constant elements or be differentiable. The differentiable equations can not be satisfied by piece-wise constant functions. @@ -115,6 +115,7 @@ \subsection{Horizontal grid} +\label{sec:spatial_discrete_horizontal_grid} \begin{figure} \begin{center}