Development of a three-dimensional grid refinement method for the application of the Lattice Boltzmann Method to high Reynolds flows

Abstract

The lattice Boltzmann method (LBM) models fluid dynamics based on kinetic theory. It discretises the continuous Boltzmann equation in velocity, space and time and solves a transport equation for particle populations. When solved on uniform Cartesian grids, this result in a highly scalable algorithm which can accurately and efficiently model unsteady and turbulent flows. However, the reliance on uniform grids makes the LBM prohibitively expensive for the simulation of high Reynolds number flows. To reduce computational costs, grid refinement is required.

A hierarchical grid refinement method with regularised coupling is introduced in this thesis, and its implementation in the open-source LBM solver OpenLB is explained. The regularised coupling restricts the information exchange at the refinement interface to the leading order terms of the particle populations. This ensures that local viscous stresses are conserved across the interface and prevents numerical instabilities. The method is validated against two benchmarks: the vortex shedding flow around a circular cylinder and the lid-driven flow inside a cubic cavity. It is demonstrated that the grid-refined methodology accurately captures the flow features at different Reynolds numbers, including two instability modes during the cylinder wake transition. Refinement reduces the number of active cells by a factor of 28 for the cylinder at Reynolds number Re=300. For the lid-driven cavity case at Re=3200, the performance efficiency and continuity across the refinement interface are assessed. The regularised coupling diminishes the transmission of spurious waves and improves numerical stability.

Finally, this method is applied with a Smagorinsky subgrid model to an open shallow cavity at Re=50,000. Good agreement between the LBM solution and reference experimental and numerical data in terms of time-average velocities and turbulence statistics exists. This successful application demonstrates that the newly implemented methods achieve accurate and stable LBM simulations at high Reynolds number with efficient use of computational resources.