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A computationally efficient method for solving three-dimensional, viscous,incompressible flows on unbounded domains is presented. The method formallydiscretizes the incompressible Navier-Stokes equations on an unboundedstaggered Cartesian grid. Operations are limited to a finite computationaldomain through a lattice Green's function technique. This technique obtainssolutions to inhomogeneous difference equations through the discreteconvolution of source terms with the fundamental solutions of the discreteoperators. The differential algebraic equations describing the temporalevolution of the discrete momentum equation and incompressibility constraintare numerically solved by combining an integrating factor technique for theviscous term and a half-explicit Runge-Kutta scheme for the convective term. Aprojection method that exploits the mimetic and commutativity properties of thediscrete operators is used to efficiently solve the system of equations thatarises in each stage of the time integration scheme. Linear complexity, fastcomputation rates, and parallel scalability are achieved using recentlydeveloped fast multipole methods for difference equations. The accuracy andphysical fidelity of solutions is verified through numerical simulations ofvortex rings.

A fast lattice Green's function method for solving viscous incompressible flows on unbounded domains