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We study the formal precision of the relative velocity lattice Boltzmannschemes. 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 ofspace and time. We deal with the asymptotics of the relative velocity schemesfor one conservation law: the third order equivalent equation is exposed for anarbitrary number of dimensions and velocities.

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