Stability and Accuracy of Lattice Boltzmann Method

TL;DRAbstract

The advection di usion and Navier Stokes equation can be recovered from Lattice Boltzmann equation. The stability and accuracy analysis need to be performed to ensure that those equations are recovered correctly. The Lattice Boltzmann stability analysis is still an open research area. The von Neumann stability is used to investigate the maximum stable velocity of multi-relaxation time (MRT) model as a function of relaxation parameters for di erent lattice models. The maximum stable velocity is the maximum velocity that keep the error bounded. The accuracy of each lattice model is investigated as a function of velocity and number of mesh points. It is noted that the maximum velocity calculated from stability analysis becomes signi cant when the relaxation parameter is approaching 2 (zero viscosity), while the maximum velocity that ensures the accuracy becomes signi cant when the relaxation parameter is away from 2.

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