Implementation of the compact interpolation within the octree based Lattice Boltzmann solver Musubi

TL;DR

This paper presents a parallel octree-based lattice Boltzmann solver with a compact interpolation scheme that improves efficiency on non-uniform meshes, validated through classical flow tests and convergence analysis.

Contribution

It introduces a second order accurate compact interpolation for grid coupling in octree-based Lattice Boltzmann methods, reducing computational overhead and enabling efficient parallel implementation.

Findings

Second order convergence validated in Taylor-Green vortex

Accurate simulation of flow around cylinder and sphere

Reduced computational and communication overhead

Abstract

A sparse octree based parallel implementation of the lattice Boltzmann method for non-uniform meshes is presented in this paper. To couple grids of different resolutions, a second order accurate compact interpolation is employed and further extended into three dimensions. This compact interpolation requires only four source elements from the adjacent level for both two- and three dimensions. Thus, it reduces the computational and communication overhead in parallel executions. Moreover, the implementation of a weight based domain decomposition algorithm and level-wise elements arrangement are explained in details. The second order convergence of both velocity and strain rate are validated numerically in the Taylor-Green vortex test case. Additionally, the laminar flow around a cylinder at Re = 20, 100 and around a sphere at Re = 100 is investigated. Good agreement between simulated results and those from literature is observed, which provides further evidence for the accuracy of our method.