Matrix lattice Boltzmann reloaded

The lattice Boltzmann equation has been introduced about twenty years ago as a new paradigm for computational °uid dynamics. In this paper, we revisit the main formulation of the lattice Boltzmann collision integral (matrix model) and introduce a new two-parametric family of collision operators which permits to combine enhanced stability and accuracy of matrix models with the outstanding simplicity of the most popular single-relaxation time schemes. The option of the revised lattice Boltzmann equation is demonstrated through numerical simulations of a three-dimensional lid driven cavity.