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A particle-in-cell ansatz for solving the Euler equations in a rotating frame is described. The approach is ideally suited for "layered" models of flows with sharp density and velocity fronts. The material and Coriolis accelerations in the Euler equations are solved at each particle while the gradient accelerations are evaluated on a grid and interpolated at each time step to the particles. The height of each particle is fixed and, depending on the application may be constant for all particles or may vary from particle to particle. The approach is used here to predict the evolution of a lens in a layered model with lower layer outcropping. The integral invariant of the volume is conserved exactly and total energy and total angular momentum are conserved to within 3% throughout a 30 day simulation. Exceptional resolution of the density and velocity fronts is maintained during the simulation without imposing any numerical viscosity. the model also reproduces essential characteristics of analytic solutions to a parabolic shaped lens. This algorithm is well suited to parallel implementation; all of the calculations reported here were done on an IBM SP2. Performance speedup and execution time as a function of the number of processors is given.