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Incompressible limits of lattice Boltzmann equations using multiple relaxation times. (English) Zbl 1076.76063
Summary: Lattice Boltzmann equations using multiple relaxation times are intended to be more stable than those using a single relaxation time. The additional relaxation times may be adjusted to suppress non-hydrodynamic modes that do not appear directly in the continuum equations, but may contribute to instabilities on the grid scale. If these relaxation times are fixed in lattice units, as in previous work, solutions computed on a given lattice are found to diverge in the incompressible (small Mach number) limit. This non-existence of an incompressible limit is analysed for an inclined one dimensional jet. An incompressible limit does exist if the non-hydrodynamic relaxation times are not fixed, but scaled by the Mach number in the same way as the hydrodynamic relaxation time that determines the viscosity.

MSC:
76M28 Particle methods and lattice-gas methods
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
Software:
FFTW; LAPACK
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