Lattice Boltzmann Algorithms for Fluid Turbulence

Lattice Boltzmann algorihms are a mesoscopic representation of nonlinear continuum physics (like Navier-Stokes, magnetohydro dynamics (MHD), Gross- Pitaevskii equations) which are ideal for parallel supercomputers because they transform the difficult nonlinear convective macroscopic derivatives into purely local moments of distribution functions. The macroscopic nonlinearities are recovered by relaxation distribution functions in the collision operator whose dependence on the macroscopic velocity is algebraically nonlinear and thus purely local. Unlike standard computational fluid dynamics codes, there is no loss in parallelization in handling arbitrary geometric boundaries, e.g., using bounce-back rules from kinetic theory. By encoding detailed balance into the collision operator through the introduction of discrete H-function, the lattice Boltzmann algorithm can be made unconditionally stable for arbitrary high Reynolds numbers. It is shown that this approach is a special case of a quantum lattice Boltzmann algorithm that entangles local qubits through unitary collision operators and which is ideally parallelized on quantum computer architectures. Here we consider turbulence simulations using 2,048 PEs on a 1,6003-spatial grid. A connection is found between the rate of change of enstrophy and the onset of laminar-to- turbulent flows.