An improved Galilean-invariant MRT-LBM for flows with mass and momentum source terms: theoretical and stability analysis

Purpose Maintaining Galilean invariance and numerical stability is essential for lattice Boltzmann simulations of flows with mass sources. This study aims to develop a multiple-relaxation-time (MRT) formulation that preserves the physically consistent coupling between mass and momentum and assess its capabilities for pressure regulation. Design/methodology/approach The single-relaxation-time (SRT) treatment of mass sources that preserves Galilean invariance is incorporated into MRT collision dynamics in moment space. Chapman–Enskog analyses are conducted in one and two dimensions. Numerical performance is evaluated using moving mass sources, standing waves with high wavenumbers and Poiseuille flow in two dimensions. Findings The analyses demonstrate recovery of the target Navier–Stokes equations with mass-source terms. In moving reference frames, the model eliminates unphysical oscillations and reduces global relative errors by approximately two orders of magnitude compared with uncorrected models across the tested scenarios. In the standing wave tests, the MRT model exhibits greater numerical robustness than the SRT model. At the largest tested inverse relaxation parameter, its maximum stable mass-source amplitude is more than three times that of the SRT model. Tests of pressure boundary implementation and pressure regulation throughout the domain show excellent agreement with analytical solutions. Originality/value This work extends an established mass-source treatment preserving Galilean invariance to an MRT framework with independently relaxed moments. The formulation supports simulations of flows with mass sources, offering improved numerical robustness under the tested conditions and capabilities for pressure regulation.