Fast convergence and asymptotic preserving of the General Synthetic Iterative Scheme

Wei Su; Lianhua Zhu; Lei Wu

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arXiv · 2003.09958

Fast convergence and asymptotic preserving of the General Synthetic Iterative Scheme

Wei Su·Lianhua Zhu·Lei Wu

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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 $K$, 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.

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Wei Su, Lianhua Zhu, Lei Wu. 2020-03-22. Fast convergence and asymptotic preserving of the General Synthetic Iterative Scheme. https://arxiv.org/abs/2003.09958

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