Proposing a lattice spring damper model for simulation of interaction between elastic/ viscoelastic filaments and fluid flow in immersed boundary-lattice Boltzmann framework

Abstract

In the present paper, a Lattice-Spring-Damper-Model (LSDM) is proposed to analyze the interactions between elastic (viscoelastic) structures and fluid flow by implementing the framework of the Immersed Boundary-Lattice Boltzmann Method. Lattice Boltzmann Method is employed for the simulation of the fluid domain, and as for deformable structures analysis, the “mass-spring-damper’’ network is proposed. In this study, a series of viscous dampers is added in mass-spring network to produce a viscoelastic solid network. This network can be readily converted into an elastic network and is able to cover various properties such as elastic modulus, bending rigidity, and rheological characteristics of viscoelastic solids. Moreover, some critical rheological tests such as creep test, oscillation test, and relaxation test are checked in the viscoelastic solids by the proposed method. To check the ability of the proposed model, the flapping dynamics of a viscoelastic filament is considered in the presence of fluid flow. Since most numerical studies have investigated the movement of the elastic filaments, this study is mainly focused on the simulation of viscoelastic deformable filaments. The elastic/viscoelastic filaments’ flapping regime are assessed and the effects of Reynolds number and geometrical parameters of the deformable filaments are analyzed and checked with the available data in the literature. Results show that the behavior of real elastic structures and viscoelastic bodies can be properly analyzed by the proposed LSDM by considering their rheometric features.