Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 197, Issue 25-28, Pages 2131-2146Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2007.08.014
Keywords
immersed boundary method; fractional step method; projection method; nullspace method; vorticity/streamfunction formulation; far-field boundary conditions; multi-domain method; fast Poisson solver; finite volume method; incompressible viscous flow
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We report on the continued development of a projection approach for implementing the immersed boundary method for incompressible flows in two and three dimensions. Boundary forces and pressure are regarded as Lagrange multipliers that enable the no-slip and divergence-free constraints to be implicitly determined to arbitrary precision with no associated time-step restrictions. In order to accelerate the method, we further implement a nullspace (discrete streamfunction) method that allows the divergence-free constraint to be automatically satisfied to machine roundoff. By employing a fast sine transform technique, the linear system to determine the forces can be solved efficiently with direct or iterative techniques. A multi-domain technique is developed in order to improve far-field boundary conditions that are compatible with the fast sine transform and account for the extensive potential flow induced by the body as well as vorticity that advects/difluses to large distance from the body. The multi-domain and fast techniques are validated by comparing to the exact solutions for the potential flow induced by stationary and propagating Oseen vortices and by an impulsively-started circular cylinder. Speed-ups of more than an order-of-magnitude are achieved with the new method. (C) 2007 Elsevier B.V. All rights reserved.
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