Third order equivalent equation for the relative velocity lattice Boltzmann schemes with one conservation law

Abstract: We study the formal precision of the relative velocity lattice Boltzmann schemes. They differ from the d'Humi`eres schemes by their relaxation phase: it occurs for a set of moments parametrized by a velocity field function of space and time. We deal with the asymptotics of the relative velocity schemes for one conservation law: the third order equivalent equation is exposed for an arbitrary number of dimensions and velocities.