A Comparative study of the cubic interpolated propagation method and the finite difference method on approximation accuracy of the lattice boltzmann equation for spatial derivative

Spatial derivative of the distribution function follows the lattice Boltzmann equation (LBE), because the advection term in the kinetic equation is linear in the lattice Boltzmann method. The cubic interpolated propagation (CIP) method and the finite difference method (FDM) are employed to discretize the kinetic equation for spatial derivative. We comparatively verify the approximation accuracy of the CIP and of the FDM with simulations of the Taylor vortex flow, of the Poiseuille flow, and of the unsteady Couette flow. The simulation result of the Taylor vortex flow reveals that the FDM indicates the 2nd-order accurate spatial convergence rate, and the applicability of the CIP method to the LBE is not good enough. The numerical simulations show that the differentiation of fluid density and of velocity is able to be calculated by a simple arithmetic calculation of the spatial derivative of the distribution function.