Purified Two-Relaxation-Time Lattice Boltzmann Method: Removing Ghost Modes from TRT for Enhanced Stability

Abstract

The two-relaxation-time (TRT) lattice Boltzmann model is widely adopted for its simplicity and tunable boundary accuracy. However, its collision operator relaxes the full symmetric non-equilibrium component, implicitly retaining non-hydrodynamic ghost modes that degrade stability at high Reynolds numbers. In this work, we establish a rigorous connection between ghost-mode filtering and regularization within the TRT framework. By decomposing the discrete velocity space into hydrodynamic and non-hydrodynamic subspaces, we prove that the TRT-regularized lattice Boltzmann (TRT-RLB) model is mathematically equivalent to the standard TRT model with ghost modes explicitly removed. This equivalence holds exactly for D2Q9 and D3Q19 lattices, where the symmetric and antisymmetric subspaces are completely spanned by the physically relevant Hermite modes and identifiable ghost modes. Based on this finding, we propose the Purified TRT (P-TRT) model, which achieves regularization-level stability through simple algebraic ghost-mode subtraction rather than expensive tensor projections. For D2Q9, the non-equilibrium collision cost is reduced from 180 to 52 floating-point operations per node, a 71% reduction. Linear stability analysis in moment space further reveals that the P-TRT operator annihilates the ghost eigenvalue, proving its spectral radius is bounded above by that of standard TRT and that stability is governed exclusively by hydrodynamic modes. Benchmarks including the double shear layer at Re up to 10^7, Taylor--Green vortex decay, force-driven Poiseuille flow, and creeping flow past a square cylinder confirm that P-TRT preserves the stability, second-order accuracy, and zero-slip boundary properties of TRT-RLB while retaining the simplicity of the TRT family.