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Published April 15, 2008 | public
Journal Article

A fast immersed boundary method using a nullspace approach and multi-domain far-field boundary conditions

Abstract

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/diffuses 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.

Additional Information

© 2007 Elsevier. Received 21 March 2007; received in revised form 3 August 2007; accepted 6 August 2007. Available online 12 September 2007. The authors thank Prof. Blair Perot for the enlightening discussions on the fractional step method. The experimental data presented in Section 2.2 were generously shared by Dr. William Dickson. This work was partially supported by the United States Air Force Office of Scientific Research (AFOSR/MURI FA9550-05-1-0369) and the National Science Foundation (DMS-0514414).

Additional details

Created:
August 22, 2023
Modified:
October 20, 2023