Journal of Computational Physics 161, 428–453 (2000) doi:10.1006/jcph.2000.6502, available online at http://www.idealibrary.com on The Blob Projection Method for Immersed Boundary Problems R. Cortez ∗,1 and M. Minion† ,2 ∗ Department of Mathematics, Tulane University, 6823 St. Charles Ave., New Orleans, Louisiana 70118; and †Department of Mathematics, Phillips Hall, CB 3250, University of North Carolina, Chapel Hill, North Carolina 27599 E-mail: ∗ cortez@math.tulane.edu and †minion@amath.unc.edu Received May 12, 1999; revised March 6, 2000 A new finite difference numerical method for modeling the interaction between flexible elastic membranes and an incompressible fluid in a two-dimensional domain is presented. The method differs from existing methods in the way the forces exerted by the membranes on the fluid are modeled. These are described by a collection of regularized point forces, and the velocity field they induce is computed directly on a regular Cartesian grid via a smoothed dipole potential. Comparisons between this method and the immersed boundary method of Peskin and McQueen are presented. The results show that the method proposed here preserves volumes better and has a higher order of convergence. c  2000 Academic Press Key Words: immersed boundaries; projection method. 1. INTRODUCTION A high-order numerical method for the solution of two-dimensional immersed boundary problems is presented. In this context, immersed boundaries refer to thin, flexible membranes within a constant density, incompressible fluid. The key feature of these problems is that both the fluid and the immersed boundary motions must be computed simultaneously, accounting for the interaction between the forces developed along the boundaries and the motion of the fluid surrounding them. Existing numerical methods for immersed boundary problems can be placed into two general categories: methods that determine the jump in the variables that are discontinuous across the boundaries (see, e.g., [16]) and methods that regularize the same variables to smooth out the jumps. The immersed boundary method introduced by Peskin and developed further by Peskin and McQueen fits into the second category 1 Supported in part by NSF Grant DMS-9816951. 2 Supported in part by the Alfred P. Sloan Foundation and by NSF Grant DMS-9973290. 428 0021-9991/00 $35.00 Copyright c  2000 by Academic Press All rights of reproduction in any form reserved.