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~\cite{SuArXiv2019}, where various numerical simulations have shown that (i) the steady-state solution can be found within dozens of iterations at any Knudsen number , 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 , 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.
Keywords
Cite
@article{arxiv.2003.09958,
title = {Fast convergence and asymptotic preserving of the General Synthetic Iterative Scheme},
author = {Wei Su and Lianhua Zhu and Lei Wu},
journal= {arXiv preprint arXiv:2003.09958},
year = {2020}
}