SIAM Journal on Scientific and Statistical Computing
Improved volume conservation in the computation of flows with immersed elastic boundaries
Journal of Computational Physics
Lattice Boltzmann method for moving boundaries
Journal of Computational Physics
Truncation error analysis of lattice Boltzmann methods
Journal of Computational Physics
The immersed boundary-lattice Boltzmann method for solving fluid-particles interaction problems
Journal of Computational Physics
Unconditionally stable discretizations of the immersed boundary equations
Journal of Computational Physics
Journal of Computational Physics
A hybrid method to study flow-induced deformation of three-dimensional capsules
Journal of Computational Physics
Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers
Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers
Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications
Journal of Computational Physics
Journal of Computational Physics
Editorial: Mesoscopic methods in engineering and science
Computers & Mathematics with Applications
Journal of Computational Physics
Journal of Computational Physics
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The deformation of an initially spherical capsule, freely suspended in simple shear flow, can be computed analytically in the limit of small deformations [D. Barthes-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.