Memory-efficient Lattice Boltzmann Method for low Reynolds number flows

TL;DR

This paper introduces a simplified, memory-efficient Lattice Boltzmann Method for low Reynolds number flows by fixing the relaxation time, reducing memory usage and implementation complexity, with tested accuracy and limitations in multiphase flows.

Contribution

A novel simplified Lattice Boltzmann algorithm that reduces memory and implementation complexity for low Reynolds number flows, inspired by MRT approaches.

Findings

Error decreases as grid size increases, following L^{-2}

The new method requires less memory and is easier to implement

Less efficient in multiphase flow simulations

Abstract

The Lattice Boltzmann Method algorithm is simplified by assuming constant numerical viscosity (the relaxation time is fixed at $\tau=1$). This leads to the removal of the distribution function from the computer memory. To test the solver the Poiseuille and Driven Cavity flows are simulated and analyzed. The error of the solution decreases with the grid size L as $L^{-2}$. Compared to the standard algorithm, the presented formulation is simpler and shorter in implementation. It is less error-prone and needs significantly less working memory in low Reynolds number flows. Our tests showed that the algorithm is less efficient in multiphase flows. To overcome this problem, further extension and the moments-only formulation was derived, inspired by the Multi-Relaxation Time (MRT) approach for single component multiphase flows.