On optimal node spacing for immersed boundary–lattice Boltzmann method in 2D and 3D

Abstract

A computational study on optimal spacing of Lagrangian nodes discretizing a rigid and immobile immersed body boundary in 2D and 3D is presented in order to show how the density of the Lagrangian points affects the numerical results of the Immersed Boundary–Lattice Boltzmann Method (IB–LBM). The study is based on the implicit velocity correction-based IB–LBM proposed by Wu and Shu (2009, 2010) that allows computing the fluid–body interaction force. However, the (original) method fails for densely spaced Lagrangian points due to ill-conditioned or even singular linear systems that arise from the derivation of the method. We propose a modification that improves the solvability of the linear systems and compare the performance of both methods using several benchmark problems. The results show how the spacing of the Lagrangian points affects the numerical results, mainly the permeability of the discretized body boundary in applications to fluid flows over rigid obstacles and blood flows in arteries in 2D and 3D.