A simple finite difference strategy

In the particular case of equal grid block sizes (Ax = Ax, = Ax.+j/2) multiplying across Equation 8.14 by the cell volume of block i Ax l) to convert to volumetric flow rates then  

The total inter-block transmissibilities in Equation 8.17 are taken as harmonic averages (Aziz and Settari, 1979 Peaceman, 1977 Crichlow, 1977) according to  

Equation 8.17 rearranges to a tridiagonal system of equations which may be solved very conveniently using the Thomas algorithm (Aziz and Settari, 1979). 

When Equation 8.17 has been solved for the pressure. Equation 8.10 is then used to update the water saturation explicitly from to 5 The 

Several schemes can be used to solve this equation, but here only a simple backward in distance (upstream)-forward in time (explicit) discretisation is presented. This gives the following explicit update equation for polymer concentration to be solved after the saturation update equation (to obtain S ). 

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