Choice of Variable Arrangement on the Grid

In this section, attention is given to the numerical discretization of the finite volume calculation domain and the choice of variable arrangement on the grid. 

In the coordinate discretization process one selects the node points in the domain at which the values of the unknown dependent variables are to be computed. In the finite volume method one also selects the location of the grid cell surfaces at which the property fluxes are determined. In this way the computational domain is sub-divided into a number of smaller, nonoverlapping sub-domains. There are many variants of the distribution of the computational node points and grid cell surfaces within the solution domain. The grid arrangements associated with the finite volume discretization of the momentum equation are generally more complicated than the one employed for a scalar transport equation. 

As a first approach, it may be natural to employ a collocated grid arrangement and store all the variables at the same set of grid points and to use the same grid volumes for all of them. In this case the number of coefficients that must be computed and stored is minimized, because many of the terms in each of the equations are essentially identical. However, it is not required that 

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