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Accuracy of discrete-velocity BGK models for the simulation of the incompressible Navier-Stokes equations. (English) Zbl 0845.76086
Since 1988 the so-called lattice Boltzmann (LB) model is used to obtain the lattice gas automata retaining a number of characteristics of the Navier-Stokes equation. In this paper, the LB method is considered as a discretization of the discrete Boltzmann equation. It is shown numerically that the employed 9-velocity scheme converges to incompressible Navier-Stokes equation. The evolution of Taylor vortices in a periodic domain is chosen as a test problem. As mentioned by the authors, the “time step restrictions require a tremendous number of computations to produce accuracy, thus degrading the overall performance of the method”.

MSC:
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
76M20 Finite difference methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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