Non-orthogonal central moments relaxing to a discrete equilibrium: A D2Q9 lattice Boltzmann model

A novel D2Q9 lattice Boltzmann scheme based on the relaxation of central moments is presented. Differently from previous efforts, here we introduce a non-orthogonal basis of moments which relax to a discrete local equilibrium. Under these choices, our proposed model recovers exactly the BGK collision kernel if a unique relaxation rate is adopted. Numerical tests involving well-consolidated canonical problems highlight the excellent properties of the algorithm in terms of accuracy, convergence and stability. Moreover, our formulation shows an intelligible derivation and a simple practical implementation.