Stable LBM schemes for acoustic scaling simulations under high Reynolds to Mach ratio: Introduction to the DM-TS operator

Abstract

Hydroacoustic analyses using direct methods are challenging in the field of computational physics. To date, hybrid methods are an alternative approach adopted for performing hydroacoustic analysis, although it demonstrates clear limitations in analyzing nonlinear turbulent noise. The lattice Boltzmann method (LBM) provides a solution to address the limitations of the hybrid method and is frequently applied in aeroacoustics. However, existing methods, such as the Bhatnagar–Gross–Krook (BGK) operator, suffer from instabilities that manifest in an oscillatory fashion in underwater conditions. Hydroacoustic situations are characterized by high Reynolds number (Re) to Mach number (Ma) ratios, and these conditions correspond to cases where stability problems occur. In this study, a direct-method-based two-step (DM-TS) LBM collision operator is introduced to solve the stability problem. The stability, accuracy, and consistency of the scheme are investigated and compared with the BGK-LBM. The DM-TS operator is developed to provide the same accuracy order as the BGK scheme while addressing the stability problem. Vortex shedding from a two-dimensional cylinder is simulated using the DM-TS operator to prove that the proposed method could be used to solve hydroacoustic problems. The results of the analysis indicate that dynamic and acoustic pressures can be obtained simultaneously using the DM–TS operator.