Stability analysis of lattice Boltzmann methods. (English) Zbl 0840.76078

We present an analysis of the stability of perturbations of the particle populations linearized about equilibrium values corresponding to a constant-density uniform mean flow. The linear stability depends on the following parameters: the distribution of the mass at a site between the different discrete speeds, the BGK relaxation time, the mean velocity, and the wave-number of the perturbations. We report some stability results for a subset of the parameter space for a 7-velocity hexagonal lattice, a 9-velocity square lattice, and a 15-velocity cubic lattice.


76M25 Other numerical methods (fluid mechanics) (MSC2010)
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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