Finite-volume lattice Boltzmann schemes in two and three dimensions

Simple and practical finite-volume schemes for the lattice Boltzmann equation are derived in two and three dimensions through the application of modern finite-volume methods. The schemes use a finite-volume vortex-type formulation based on quadrilateral elements in two dimensions and trilinear hexahedral elements in three dimensions. It is shown that the schemes are applicable to domains with irregular boundaries of arbitrary shape in two and three dimensions.