Comparison of Spectral Method and Lattice Boltzmann Simulations of Two-Dimensional Hydrodynamics

We present numerical solutions of the two-dimensional Navier-Stokes equations by two methods; spectral and the novel Lattice Boltzmann Equation (LBE) scheme. Very good agreement is found for global quantities as well as energy spectra. The LBE scheme is, indeed, providing reasonably accurate solutions of the Navier-Stokes equations with an isothermal equation of state, in the nearly incompressible limit. Relaxation to a previously reported ``sinh-Poisson’’ state is also observed for both runs.