I tried to generete nonuniform mesh in lattice boltzmann.
My basic articles are:
He, X., Luo, L.-S., Dembo, M., Some Progress in Lattice Boltzmann Method. Part I. Nonuniform Mesh Grids, Journal of Computational Physics, 129, 1996, pp.357-363
He, X., Luo, L.-S., Dembo, M., Some progress in the lattice Boltzmann method: Reynolds number enhancement in Simulations, Journal of Physics A, Vol. 239, 1997, pp. 276-285.
In these articles; two interpolation scheme are used: First, second-order upwind interpolation is used in the interior channel (channel floe is studied in this article), second, second order central difference interpolation is applied to the mesh grids next to the boundaries.
Please, give me any detail about second order interpolation and central difference interpolation.