Abstract
A Hele Shaw cell contains two fluids seperated by an interface. Because the fluids are held in a narrow regions between two plates the cell can be described by a set of two-dimensional hydrodynamic equations, which determine the velocity fields in the fluids as well as the motion of the interface between them. A discretized version of these equations can be implemented in terms of the motion of random walkers. The walkers have the effect of carrying pieces of the fluid from one place to another. They simulate a discrete version of the Laplace equation and obey the appropriate boundary conditions for the fluid. The walker-hydrodynamic connection is explored in the limiting situation in which the viscosity of one of the fluids vanishes. An algorithm is constructed and a few exemplary simulations are shown.
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Kadanoff, L.P. Simulating hydrodynamics: A pedestrian model. J Stat Phys 39, 267–283 (1985). https://doi.org/10.1007/BF01018663
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DOI: https://doi.org/10.1007/BF01018663