Fast convergence and asymptotic preserving of the General Synthetic Iterative Scheme
Abstract
Recently the general synthetic iteration scheme (GSIS) is proposed to find the steady-state solution of the Boltzmann equation~SuArXiv2019, where various numerical simulations have shown that (i) the steady-state solution can be found within dozens of iterations at any Knudsen number K, and (ii) the solution is accurate even when the spatial cell size in the bulk region is much larger than the molecular mean free path, i.e. Navier-Stokes solutions are recovered at coarse grids. The first property indicates that the error decay rate between two consecutive iterations decreases to zero with K, while the second one implies that the GSIS is asymptotically preserving the Navier-Stokes limit. This paper is dedicated to the rigorous proof of both properties.