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 ...

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...

in this study, we proposed a novel scheme for the implementation of the no-slip boundary condition in thelattice boltzmann method (lbm) . in detail , we have substituted the classical bounce-back idea by the direct immersed boundary specification . in this way we construct the equilibrium density functions in such a way that it feels the no-slip boundaries . therefore , in fact a kind of equili...

Mathematical modelling provides a useful framework within which to investigate the organization of biological tissues. With advances in experimental biology leading to increasingly detailed descriptions of cellular behavior, models that consider cells as individual objects are becoming a common tool to study how processes at the single-cell level affect collective dynamics and determine tissue ...

A projection-based immersed boundary method is dominated by sparse linear algebra routines. Using the open-source Cusp library, we observe a speedup (with respect to a single cpu core) which reflects the constraints of a bandwidth-dominated problem on the gpu. Nevertheless, gpus offer the capacity to solve large problems on commodity hardware. This work includes validation and a convergence stu...

Electric field induced particle-particle interactions and assembly are of great interest due to their useful applications in micro devices. The behavior of particles becomes more complex if multiple particles interact with each other at the same time. In this paper, we present a numerical study of two dimensional DC dielectrophoresis based particle-particle interactions and assembly for multipl...

The Immersed Boundary method is one of the most useful computational methods in studying fluid structure interaction. On the other hand, the Immersed Boundary method is also known to require small time steps to maintain stability when solved with an explicit method. Many implicit or approximately implicit methods have been proposed in the literature to remove this severe time step stability con...

In the present study, the combination of lattice Boltzmann and immersed boundary methods is used to simulate the motion and deformation of a flexible body. Deformation of the body is studied in microchannel with stenosis and the effect of the flexibility changes on its deformation is investigated. The obtained results in the present manuscript show that by increasing the elasticity modulus, the...

A novel immersed boundary velocity correction–lattice Boltzmann method is presented and validated in this work by its application to simulate the two-dimensional flow over a circular cylinder. The present approach is inspired from the conventional immersed boundary method (IBM). In the conventional IBM, the effect of rigid body on the surrounding flow is modeled through a forcing term, which is...