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Viscosity of finite difference lattice Boltzmann models. (English) Zbl 1062.76556
Summary: Two-dimensional finite difference lattice Boltzmann models for single-component fluids are discussed and the corresponding macroscopic equations for mass and momentum conservation are derived by performing a Chapman-Enskog expansion. In order to recover the correct mass equation, characteristic-based finite difference schemes should be associated with the forward Euler scheme for the time derivative, while the space centered and second-order upwind schemes should be associated to second-order schemes for the time derivative. In the incompressible limit, the characteristic based schemes lead to spurious numerical contributions to the apparent value of the kinematic viscosity in addition to the physical value that enters the Navier-Stokes equation. Formulae for these spurious numerical viscosities are in agreement with results of simulations for the decay of shear waves.

MSC:
76M28 Particle methods and lattice-gas methods
76M20 Finite difference methods applied to problems in fluid mechanics
82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
Software:
HE-E1GODF
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