A lattice-Boltzmann scheme for Cattaneo's diffusion equation

A lattice-Boltzmann (LB) formulation is developed for the simulation of Cattaneo's diffusion equation. To do this, the collision term is computed from a 1-step back relaxation dynamics which, in turn, induces a hyperbolic-type diffusion effect. The Fickian LB formulation is recovered in the limit as a relaxation time coefficient goes to zero.