A fluctuating lattice Boltzmann scheme for the one-dimensional KPZ equation

Based on the well-known mapping between the Burgers equation with noise and the Kardar–Parisi–Zhang (KPZ) equation for fluctuating interfaces, we develop a fluctuating lattice Boltzmann (LB) scheme for growth phenomena, as described by the KPZ formalism. A very simple LB-KPZ scheme is demonstrated in 1+1 spacetime dimensions, and is shown to reproduce the scaling exponents characterizing the growth of one-dimensional fluctuating interfaces.