Nonlinear fourth order Taylor expansion of lattice Boltzmann schemes

We propose a formal expansion of multiple relaxation times lattice Boltzmann schemes in terms single infinitesimal numerical variable. The result is system partial differential equations for the conserved moments scheme. presented nonlinear case up to fourth order accuracy. asymptotic corrections nonconserved are developed equilibrium values and differentials moments. Both expansions coupled conduct explicit compact formulas. new algebraic expressions validated with previous results obtained this framework. example isothermal D2Q9 scheme illustrates theoretical