A Lattice Boltzmann dynamic-Immersed Boundary scheme for the transport of deformable inertial capsules in low-Re flows

TL;DR

This paper introduces a novel lattice Boltzmann immersed boundary method for simulating the transport and deformation of inertial capsules in low-Reynolds-number flows, validated through various benchmark tests and deformable object simulations.

Contribution

It combines a BGK-Lattice Boltzmann approach with a dynamic-Immersed Boundary method and moving least squares reconstruction for accurate simulation of deformable inertial capsules.

Findings

Validated against benchmark data for rigid and deformable objects.

Demonstrated existence of a critical Reynolds number for particle revolution.

Analyzed deformation and tumbling of deformable spheroids under shear.

Abstract

In this work, a dynamic-Immersed--Boundary method combined with a BGK-Lattice--Boltzmann technique is developed and critically discussed. The fluid evolution is obtained on a three-dimensional lattice with 19 reticular velocities (D3Q19 computational molecule) while the immersed body surface is modeled as a collection of Lagrangian points responding to an elastic potential and a bending resistance. A moving least squares reconstruction is used to accurately interpolate flow quantities and the forcing field needed to enforce the boundary condition on immersed bodies. The proposed model is widely validated against well known benchmark data for rigid and deformable objects. Rigid transport is validated by computing the settling of a sphere under gravity for five different conditions. Then, the tumbling of inertial particles with different shape is considered, recovering the Jefferey orbit for a prolate spheroid. Moreover, the revolution period for an oblate spheroid and for a disk-like particle is obtained as a function of the Reynolds number. The existence of a critical Reynolds number is demonstrated for both cases above which revolution is inhibited. The transport of deformable objects is also considered. The steady deformation of a membrane under shear for three different mechanical stiffness is assessed. Then, the tumbling of a weakly-deformable spheroid under shear is systematically analyzed as a function strain stiffness, bending resistance and membrane mass.