The immersed boundary method is a computational framework for problems involving the interaction of a fluid and immersed elastic structures. Immersed boundary computations typically evaluate the elastic forces explicitly in the configuration of the immersed elastic structure. In many applications this results in a severe restriction on the time step. We present a semi-implicit and a fully impli...

In this paper we consider a modiication of the immersed boundary method based on a nite element approximation of the uid. Besides some theoretical considerations, we present two dimensional numerical examples which connrm the good behavior of the computed solutions.

Article history: Received 16 November 2010 Received in revised form 15 February 2011 Accepted 9 March 2011 Available online 16 March 2011

Article history: Received 7 April 2016 Received in revised form 10 November 2016 Accepted 25 November 2016 Available online 29 November 2016

Article history: Received 31 January 2011 Received in revised form 17 August 2011 Accepted 6 November 2011 Available online 16 November 2011

A linear stability analysis is performed on a two-dimensional version of the \immersed ber problem", formulated by C. Peskin to model the ow of uid in the presence of a mesh of moving, elastic bers. The purpose of the analysis is to isolate the modes in the solution which are associated with the ber, and thereby determine the eeect of the presence of a ber on the uid. The results are used not o...

Many insects are able to sense their surrounding fluid environment through induced motion of their filiform hairs. The mechanism by which the insect can sense a wide range of input signals using the canopy of filiform hairs of different length and orientation is of great interest. Most of the previous filiform hair models have focused on a single, rigid hair in an idealized air field. We have d...

The method of geodesic expansions is systematically explained. Based on the Haar measures of the group of geodesic expansions the semiclassical sum over immersed manifolds is constructed. Gauge fixing is performed via the Faddeev Popov method.

In this paper, we develop an immersed boundary (IB) method to simulate the dynamics of inextensible vesicles interacting with an incompressible fluid. In order to take into account the inextensibility constraint of the vesicle, the penalty immersed boundary (pIB) method is used to virtually decouple the fluid and vesicle dynamics. As numerical tests of our current pIB method, the dynamics of si...

Article history: Received 16 July 2016 Received in revised form 30 January 2017 Accepted 8 February 2017 Available online 14 February 2017