An Eulerian based geometry conforming grid-block dynamic mesh refinement for the lattice Boltzmann method

Abstract

An algorithm for a three-dimensional fine-grid block encompassing a moving solid body using a multi-relaxation time model of the lattice Boltzmann method is proposed and developed. In this numerical framework, a geometry-conforming fine block shifts a coarse lattice unit as the object translates by same amount. The effective utilization of higher-order spatial interpolation has been demonstrated in place of the commonly used low-order temporal interpolation in traditional grid refinement techniques within the lattice Boltzmann method. The successful application of this method has been showcased through three distinct cases: the settling of a solid sphere in a fluid tank under the influence of gravity, hovering motion of an elliptic airfoil, and the “clap and fling” motion of an insect wing. In this regard, various interpolation schemes based on the location of nodes in the overlapping zones of fine and coarse block are discussed. In addition, two cases were evaluated, case 1 where distributions are interpolated and case 2 where macroscopic variables are directly interpolated. It was observed that both interpolations gave same computational accuracy for low Reynolds number [∼O(102)]. However, as Re is increased [∼O(103)], direct interpolation of macroscopic variables proved erroneous and resulted in a large deviation in fluid forces and is not recommended. The geometry-conforming dynamic mesh refinement results in a substantial decrease in computation time, approximately 90%, along with a memory reduction of about 80% compared to the fully refined counterpart.