A cellular automata simulation of two-phase flow on the CM-2 Connection Machine computer

A cellular automaton (CA) recently developed by D.H. Rothman and J.M. Keller (1988) simulates the flow of two incompressible, immiscible, viscous fluids in two dimensions. This automaton has been simulated on the CM-2 Connection Machine using a sequence of logical operations and table lookups to determine the state of a CA site from its old state and those of its neighbors. The logical operations are performed in parallel by each of the Connection Machine processors, while the table lookups use the indirect addressing capabilities among groups of 32 processors. A description is given of CA fluids, including the issue of isotropy, the choice of a rule set, and the averaging procedure used to obtain hydrodynamical quantities. The CM-2 Connection Machine is then described, with emphasis on the indirect addressing capabilities of the machine. A complete description is also given of the Rothman-Keller model for two-phase flow. It is shown how the indirect addressing is used in the simulation algorithm, and how a symmetry in the dynamics is used to reduce the size of the lookup tables by a factor of six. A time sequence of results showing the separation of two immiscible phases from an initially homogenized state is presented.<
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