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In this contribution, a new class of lattice Boltzmann schemes is introducedand studied. These schemes are presented in a framework that generalizes themultiple relaxation times method of d'Humi\`eres. They extend also the Geier'scascaded method. The relaxation phase takes place in a moving frame involving aset of moments depending on a given relative velocity field. We establish withthe Taylor expansion method that the equivalent partial differential equationsare identical to the ones obtained with the multiple relaxation times method upto the second order accuracy. The method is then performed to derive theequivalent equations up to third order accuracy.

Lattice Boltzmann schemes with relative velocities