Efficient and accurate simulations of deformable particles immersed in a fluid using a combined immersed boundary lattice Boltzmann finite element method

Abstract

a b s t r a c tThe deformation of an initially spherical capsule, freely suspended in simple shear flow, can be computed analytically in the limit of small deformations [D. Barthés-Biesel, J.M. Rallison, The time-dependent deformation of a capsule freely suspended in a linear shear flow, J. Fluid Mech. 113 (1981) 251-267]. Those analytic approximations are used to study the influence of the mesh tessellation method, the spatial resolution, and the discrete delta function of the immersed boundary method on the numerical results obtained by a coupled immersed boundary lattice Boltzmann finite element method. For the description of the capsule membrane, a finite element method and the Skalak constitutive model [R. Skalak, A. Tozeren, R.P. Zarda, S. Chien, Strain energy function of red blood cell membranes, Biophys. J. 13 (1973) 245-264] have been employed. Our primary goal is the investigation of the presented model for small resolutions to provide a sound basis for efficient but accurate simulations of multiple deformable particles immersed in a fluid. We come to the conclusion that details of the membrane mesh, as tessellation method and resolution, play only a minor role. The hydrodynamic resolution, i.e., the width of the discrete delta function, can significantly influence the accuracy of the simulations. The discretization of the delta function introduces an artificial length scale, which effectively changes the radius and the deformability of the capsule. We discuss possibilities of reducing the computing time of simulations of deformable objects immersed in a fluid while maintaining high accuracy.

Long-lived anomalous thermal diffusion induced by elastic cell membranes on nearby particles

“…The neo-Hookean model is characterized by a single parameter containing the membrane elastic shear and area dilatation modulus, while the Skalak model [45] uses two separate parameters for shear and area dilatation resistance, respectively. The strain energy in the Skalak model reads [61] …”

Hydrodynamic mobility of a solid particle near a spherical elastic membrane: Axisymmetric motion

“…6 b), we show the scaled self-mobility correction for C = 1 and C = 100. A very large C is typical for vesicles or red blood cells [80][81][82] where the surface area remains almost unchanged during deformation. We observe that the effect of area expansion is more pronounced in the high frequency regime.…”

Lift and thrust generation by a butterfly-like flapping wing–body model: immersed boundary–lattice Boltzmann simulations

“…Feng & Michaelides 2004, 2005Shu et al 2007;Sui et al 2008;Wu & Shu 2010;Kruger et al 2011). The authors also proposed a new IB-LBM (Suzuki & Inamuro 2011), which is more accurate for satisfying the no-slip boundary condition at a moving boundary than other IB-LBMs.…”