We consider the problem of “energy conserving” lattice Boltzmann models. A major difficulty observed in previous studies is the coupling between the viscous and thermal waves even at moderate wave numbers. We propose a theoretical framework based on the knowledge of the partial equivalent equations of the lattice Boltzmann scheme at several orders of precision. With the help of linearized model...

We present a finite-volume formulation for the lattice Boltzmann method (FVLBM) based on standard bilinear quadrilateral elements in two dimensions. The accuracy of this scheme is demonstrated by comparing the velocity field with the analytical solution of the Navier-Stokes equations for time dependent rotating Couette flow and Taylor vortex flow. To demonstrate the flexibility of the scheme, w...

Both the artificial compressibility method and the lattice Boltzmann method yield the solutions of the incompressible Navier-Stokes equations in the limit of the vanishing Mach number. The inclusion of the bulk viscosity is one of the reasons for the success of the lattice Boltzmann method since it removes quickly the acoustic mode, which inevitably appears as the compressible effect, and contr...

The lattice Boltzmann equation was introduced about 20 years ago as a new paradigm for computational fluid 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 us to combine enhanced stability and accuracy of matrix models with the outstanding simplicity...

Both the artificial compressibility method and the lattice Boltzmann method yield the solutions of the incompressible Navier-Stokes equations in the limit of the vanishing Mach number. The inclusion of the bulk viscosity is one of the reasons for the success of the lattice Boltzmann method since it removes quickly the acoustic mode, which inevitably appears as the compressible effect, and contr...