The Blob Projection Method for Immersed Boundary Problems

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.