Utilization of pressure wave-dynamics in accelerating convergence of the lattice-Boltzmann method for steady and unsteady flows

Abstract

The lattice-Boltzmann method, in its classical form, is a hyperbolic-leaning equation system which requires long term time-marching solutions to attain quasi-steady state, and much research has been done to improve the convergence performance of the algorithm. Nevertheless, previous approaches have seen limited use in the literature, either due to high complexity, a lack of integrability, and/or instability considerations. In this study, we propose a new acceleration scheme that utilizes information carried by pressure waves propagating in the simulated domain to achieve accelerated convergence to steady and quasi-steady state solutions. The formulated algorithm achieves accurate final flow fields and is in excellent agreement for tested benchmark problems. We show that this scheme is highly robust for a wide range of relaxation parameters in the single-relaxation time and the multiple-relaxation time formulations of the LBM, and effectively apply the algorithm to both obstacle-driven and shear-driven flows, with an observed time reduction to steady state behavior of more than half. Furthermore, the method is successfully tested on a complex, unsteady flow employing the KBC entropic multirelaxation operator – this exhibited a significant reduction of the flow transient stage of up to 63.8%, and proves the scheme to work with the full triad of major LB collision operators. In terms of numerical implementation, the relative cleanness and ‘bolt-on’ nature of the proposed algorithm allows for ease of application and increased universality, making it ideal for a previously unfilled role in current LBM development.