Efficient lattice Boltzmann models for the Kuramoto-Sivashinsky equation

TL;DR

This paper presents an improved lattice Boltzmann model for the Kuramoto-Sivashinsky equation that enhances stability and accuracy, allowing larger time steps and significantly better performance compared to previous models.

Contribution

The authors develop a more stable and accurate lattice Boltzmann scheme using higher lattice speeds and modified parameters, outperforming earlier models in efficiency.

Findings

92% performance improvement on D1Q7 lattice

Enhanced stability allows larger time steps

Maintains accuracy despite increased time increments

Abstract

In this work, we improve the accuracy and stability of the lattice Boltzmann model for the Kuramoto-Sivashinsky equation proposed in \cite{2017_Otomo}. This improvement is achieved by controlling the relaxation time, modifying the equilibrium state, and employing more and higher lattice speeds, in a manner suggested by our analysis of the Taylor-series expansion method. The model's enhanced stability enables us to use larger time increments, thereby more than compensating for the extra computation required by the high lattice speeds. Furthermore, even though the time increments are larger than those of the previous scheme, the same level of accuracy is maintained because of the smaller truncation error of the new scheme. As a result, total performance with the new scheme on the D1Q7 lattice is improved by 92 $\%$ compared to the original scheme on the D1Q5 lattice.