Abstract: A lattice Boltzmann model was proposed for the eddy-stream system in the incompressible flows. Using two distribution functions to define the vortices and stream function, we obtained two lattice Boltzmann equations to build this model. Our equilibrium distribution function is simpler than the ones in the standard lattice Boltzmann model. As a numerical example, we obtained a good cavity flow pattern.

Key words: lattice Boltzmann equation, incompressible flows, eddy-current system