An Investigation into the Numerical Robustness of High-order Lattice Boltzmann Models

The lattice Boltzmann (LB) method has progressively emerged as a viable numerical tool for studying the dynamics of fluid flows, gaining tremendous popularity given its simplicity, adaptability, and low computational costs associated with solving the Navier-Stokes (NS) equation and beyond. The recent integration of high-order LB models, containing larger quantities of discrete velocity terms have been found to provide enhanced numerical accuracy and stability. Fundamental opportunities for further developments in assessing the performance of these lattices is imperative for future progression and applications involving complex flows, such as turbulence modelling and multiphase mixtures. However, there is still little known when comparing the performance of different high-order models. To this aim, this work presents a numerical investigation into the accuracy and stability of different high-order lattice structures, using the double-shear layer (DSL) benchmark test. The results show that lattice structures with a larger quantity of discrete velocity terms are able to produce more stable and accurate results despite possessing the same order of equilibrium terms and isotropy gradients. Further highlighted is the stability dependence of certain lattice structures on their respective reference temperature. These findings serve to provide a preliminary understanding of when to apply certain lattice structures for specific applications.