The cumulant lattice Boltzmann equation in three dimensions: Theory and validation.

We propose, analyze, and validate a lattice Boltzmann model with a cumulant collision operator. The new model is analytically and numerically shown to poses smaller errors than a moment based Multiple Relaxation Time lattice Boltzmann model. We demonstrate the usability of the cumulant lattice Boltzmann model by simulations of flow around a sphere for Reynolds numbers from 200 to 105.