We present a multi-scale lattice Boltzmann scheme, which adaptively refines particles' velocity space. Different sets of lower and higher order are consistently efficiently coupled, allowing us to use the higher-order model only when where needed. This includes regions high Mach or Knudsen numbers. The coupling procedure discrete consists either projection populations onto lower-order lifting B...

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...

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...

A lattice Boltzmann method for axisymmetric multiphase flows is presented and validated. The method is capable of accurately modeling flows with variable density. We develop the classic Shan-Chen multiphase model [Phys. Rev. E 47, 1815 (1993)] for axisymmetric flows. The model can be used to efficiently simulate single and multiphase flows. The convergence to the axisymmetric Navier-Stokes equa...

in English An introduction is given to the lattice Boltzmann method and its background, with a view towards acoustic applications of the method. To make a larger range of acoustic applications possible, a point source method is proposed. This point source is applied to simulate cylindrical waves and plane waves, and is shown to give a very good numerical result compared with analytic solutions ...