Lattice kinetic Scheme
The lattice kinetic scheme for the incompressible viscous flows was first proposed by T. Inamuro. This scheme is based on the idea that if the dimensionless relaxation time in the LBM with BGK model is set to the unity, the macroscopic variables such as velocity components and density instead of the density distribution functions become the dependent variables in the computation. As compared to the standard LBM, this scheme can save computer memory because there is no need to store the density distribution functions. The implementation of the boundary condition is very easy since on the boundaries, only the macroscopic variables rather than the density distributions are needed as for the conventional NS solvers. This feature is very useful when the flow problems with complex geometry are concerned.
The original work of T. Inamuro is limited to the uniform grid. In order to extend the scheme to be used on arbitrary meshes, we developed a new lattice kinetic scheme, which follows the idea of the Taylor series expansion- and least square- based LBM (TLLBM). The final form is an algebraic formulation, in which the coefficients only depend on the coordinates of the mesh points and lattice velocity, and can be computed once in advance. The basic formulations are shown below. For details, see references
References:
Y. Peng, C. Shu, Y. T. Chew and T. Inamuro, (2004), 'A lattice kinetic scheme for the incompressible viscous thermal flows on arbitrary meshes', Physical Review E, 69, (1) 016703.
Y. Peng, C. Shu, Y. T. Chew and H. W. Zheng, 'New lattice kinetic schemes for incompressible viscous flows', International Journal of Modern Physics C, in press.