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Lattice BGK model for incompressible Navier-Stokes equation. (English) Zbl 0979.76069
Summary: Most of the existing lattice Boltzmann BGK models (LBGK) can be viewed as compressible schemes to simulate incompressible fluid flows. The compressible effect might lead to some undesirable errors in numerical simulations. In this paper we design a LBGK model without compressible effect for simulating incompressible flows. The incompressible Navier-Stokes equations are exactly recovered from this incompressible LBGK model. Numerical simulations of plane Poiseuille flow, unsteady two-dimensional shear decaying flow, driven cavity flow, and flow around circular cylinder are performed. The results agree well with analytic solutions and with numerical results of previous studies.
76M28Particle methods and lattice-gas methods (fluid mechanics)
76D05Navier-Stokes equations (fluid dynamics)