Abstract
Flexible gridding has the potential of increasing the accuracy in numerical simulation of flow through hydrocarbon reservoirs within limitations in computing time and memory space. The adaptive gridding method presented here follows general concepts outlined by Brandt ( Math. Comput. 31, 333 (1977)). The pressure equation is discretised on locally refined grids with mixed finite elements. A multi-grid solution method is stated for the (indefinite) set of equations in the pressure and its gradient (or flow). A proof of convergence of the multi-grid process is given and convergence rates are discussed. The method has been tested on a set of equations representative for reservoir simulation. Results obtained for a five spot example are shown.
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