A lattice Boltzmann scheme with equilateral triangles for diffusion and acoustics

This contribution studies the Boltzmann scheme on a ``D2T4''grid constructed on meshes using equilateral triangles. The center of each triangle is connected to itself and to three other triangles via the edges of the mesh. We adopt the multiple relaxation time approach. Applications for diffusion and acoustics problems are considered. Consistency analysis is particularly delicate. We propose an approach based on taking bipoints into account. We derive equivalent partial differential equations for diffusion and acoustics. These systems of equations are then approximated numerically using the D2T4 lattice Boltzmann method. A comparison with an analytical calculation in the case of periodic boundary conditions shows the convergence of the D2T4 lattice Boltzmann scheme.