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Published August 10, 2007 | public
Journal Article

The Immersed Boundary Method: A Projection Approach

Abstract

A new formulation of the immersed boundary method with a structure algebraically identical to the traditional fractional step method is presented for incompressible flow over bodies with prescribed surface motion. Like previous methods, a boundary force is applied at the immersed surface to satisfy the no-slip constraint. This extra constraint can be added to the incompressible Navier–Stokes equations by introducing regularization and interpolation operators. The current method gives prominence to the role of the boundary force acting as a Lagrange multiplier to satisfy the no-slip condition. This role is analogous to the effect of pressure on the momentum equation to satisfy the divergence-free constraint. The current immersed boundary method removes slip and non-divergence-free components of the velocity field through a projection. The boundary force is determined implicitly without any constitutive relations allowing the present formulation to use larger CFL numbers compared to some past methods. Symmetry and positive-definiteness of the system are preserved such that the conjugate gradient method can be used to solve for the flow field. Examples show that the current formulation achieves second-order temporal accuracy and better than first-order spatial accuracy in L2-norms for one- and two-dimensional test problems. Results from two-dimensional simulations of flows over stationary and moving cylinders are in good agreement with those from previous experimental and numerical studies.

Additional Information

© 2007 Elsevier. Received 11 April 2006; received in revised form 11 December 2006; accepted 12 March 2007; available online 19 March 2007. The authors thank Prof. Blair Perot for the enlightening discussions on the fractional step method. This work was supported by the United States Air Force Office of Scientific Research (AFOSR/MURI FA9550-05-1-0369).

Additional details

Created:
August 19, 2023
Modified:
October 20, 2023