We present an efficient and accurate immersed boundary (IB) finite element (FE) method for numerically solving the incompressible Navier–Stokes equations. Particular emphasis is given to internal flows with complex geometries (blood flow in vasculature system). IB methods are computationally costly flows, mainly due large percentage of grid points that lie outside domain. In this study, we appl...

This paper constitutes an extension of the work of Mendez, Gibaud & Nicoud: An unstructured solver for simulations of deformable particles in flows at arbitrary Reynolds numbers, Journal of Computational Physics, 256(1): 465-483 (2014), for three-dimensional simulations of deformable membranes under flow. An immersed thick boundary method is used, combining the immersed boundary method with a t...

A modified immersed-boundary method is developed using the direct-forcing concept. An improved bilinear interpolation/extrapolation algorithm is implemented for more accurate boundary forcing expressions and easier implementation. Detailed discussions of the method are presented on the stability, velocity interpolation on the immersed boundary, directforcing extrapolation to the grid points, re...

Abstract. In this paper a direct correspondence is made between the effective stochastic dynamics of elastic structures of an Immersed Boundary Method incorporating thermal fluctuations and Stokesian-Brownian Dynamics. The correspondence is made in the limit of small Reynolds number, in which the fluid relaxes rapidly on the time scale of the motion of the immersed structures, by performing an ...

We first propose an adaptive immersed finite element method based on the a posteriori error estimate for solving elliptic equations with non-homogeneous boundary conditions in general Lipschitz domains. The underlying finite element mesh need not fit the boundary of the domain. Optimal a priori error estimate of the proposed immersed finite element method is proved. The immersed finite element ...