Application of the Connection Machine to flow and transport problems in three-dimensional heterogeneous aquifers

Abstract This paper explores the possibility of using the Connection Machine CM-2 for three-dimensional groundwater flow and transport problems in randomly heterogeneous aquifers. The steady-state flow problem is discretized using traditional finite differences and a conjugate gradient method is used to solve the resulting algebraic system. The transport problem is solved using the random walk particle tracking method (RWPTM); both reactive and non-reactive transport is examined. Although both methods appear to be well suited for the Connection Machine (CM), the flow problem, as has been demonstrated by other authors, is a clear winner on the CM, achieving speed-ups of close to 3 over the Cray Y-MP (single processor) for some problems. However, the RWPTM does not exhibit good performance because the heterogenity of the problem creates intense interprocessor communication when velocities are assigned to each particle. Because the particle distribution is non-uniform and the velocity field is large, this interprocessor communication is arbitrary. Simple vector valued subscripting was found to perform better than the several more complicated alternatives investigated for this communication step. Although the Cray Y-MP performance for the particle tracking problem was significantly better than the CM, it is nowhere near ideal because perfect vectorization is not achieved due to the large number of conditional statements (or IF statements) in the reactive part of the code.