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”.


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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