A composite multigrid method for calculating unsteady incompressible flows in geometrically complex domains

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Abstract
A time‐accurate, finite volume method for solving the three‐dimensional, incompressible Navier‐Stokes equations on a composite grid with arbitrary subgrid overlapping is presented. The governing equations are written in a non‐orthogonal curvilinear co‐ordinate system and are discretized on a non‐staggered grid. A semi‐implicit, fractional step method with approximate factorization is employed for time advancement. Multigrid combined with intergrid iteration is used to solve the pressure Poisson equation. Inter‐grid communication is facilitated by an iterative boundary velocity scheme which ensures that the governing equations are well‐posed on each subdomain. Mass conservation on each subdomain is preserved by using a mass imbalance correction scheme which is secondorder‐accurate. Three test cases are used to demonstrate the method's consistency, accuracy and efficiency.