Error analysis for the interpolation-supplemented lattice-Boltzmann equation scheme

The numerical error of the interpolation-supplemented lattice-Boltzmann equation (ISLBE) scheme is theoretically analyzed. The ISLBE is proved to recover the Navier-Stokes equation as long as a second order interpolation scheme is used and the dow domain is appropriately discretized. Using a linear interpolation scheme will inevitably generate the numerical diffusivity and viscosity, making the ISLBE scheme unable to simulate the Navier-Stokes equation correctly. The analysis is consistent with previous numerical experiments.