We explore the theoretical foundations for the inclusion of thermal fluctuations in the immersed boundary method for simulating microscale fluid systems with immersed flexible structures, as in cellular and subcellular biology. We investigate in particular the physical validity of the thermal forcing scheme with respect to the coupling of fluid and immersed structural degrees of freedom and non...

Many real-world examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen and the intracellular trafficking of vesicles into dendritic spines, involve the near-contact of elastic structures separated by thin layers of fluid. Motivated by such problems, we introduce an immersed boundary method that uses elements of lubrication theory...

When an elastic filament spins in a viscous incompressible fluid it may undergo a whirling instability, as studied asymptotically by Wolgemuth, Powers, and Goldstein [Phys. Rev. Lett., 84 (2000), pp. 16–23]. We use the immersed boundary (IB) method to study the interaction between the elastic filament and the surrounding viscous fluid as governed by the incompressible Navier–Stokes equations. T...

Article history: Received 30 October 2012 Received in revised form 14 June 2013 Accepted 13 October 2013 Available online 18 October 2013

This paper describes a formally second-order accurate version of the immersed boundary method and its application to the computer simulation of blood ow in a three-dimensional model of the human heart.

We have introduced a modified penalty approach into the flow-structure interaction solver that combines an immersed boundary method (IBM) and a multi-block lattice Boltzmann method (LBM) to model an incompressible flow and elastic boundaries with finite mass. The effect of the solid structure is handled by the IBM in which the stress exerted by the structure on the fluid is spread onto the coll...

High-order polynomial approximations of discontinuous functions give rise to oscillations in the vicinity of the discontinuity known as Gibbs phenomenon. Enrichment of the basis using discontinuous functions is shown to remove these oscillations and to recover the convergence properties generally associated with the spectral approximation of smooth functions. The convergence properties of the e...

Abstract In this paper, a Moving-Least-Squares (MLS)-based immersed boundary method (IBM) for simulating viscous compressible flows is proposed. For method, the lattice Boltzmann flux solver (LBFS) used to solve flow field on Eulerian mesh and MLS-based IBM introduced in present paper implement condition. The discrete Lagrangian points are represent Solid boundaries. A second-order MLS interpol...

The jump is defined as [∇u · n] = ∇u · n +∇u ·n where u = u|Ω± and n is the unit outward pointing normal to Ω (see figure 1). Also, we denote [u] = u − u. Many numerical methods have been developed for problem (1.1). Perhaps the most notable ones are the finite difference method of Peskin [18] (i.e., immersed boundary method) and the method of LeVeque and Li [11] (i.e., the immersed interface m...

We present a collision model for particle-particle and particle-wall interactions in interface-resolved simulations of particle-laden flows. Three types of interparticle interactions are taken into account: (1) long- and (2) short-range hydrodynamic interactions, and (3) solid-solid contact. Long-range interactions are incorporated through an efficient and second-order-accurate immersed boundar...