This paper describes a new approach to the direct numerical simulation of particle flows and illustrates its performance on several examples. The method uses a fixed regular orthogonal grid and combines an analytic solution, valid in the neighborhood of each particle, with a finite-difference solution away from the particle. In effect, the analytic solution is used to ‘transfer’ the boundary conditions at the particle surface to the neighboring grid nodes, thus eliminating the complexity arising from the incompatibility of the particle geometry with that of the underlying fixed grid. Furthermore, the hydrodynamic force and couple on the particle are computed directly with no need for the error-prone extrapolation or interpolation procedures necessary with other methods.

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