论文标题
一般合成迭代方案的快速收敛和渐近保存
Fast convergence and asymptotic preserving of the General Synthetic Iterative Scheme
论文作者
论文摘要
最近，提出了一般的合成迭代方案（GSI），以找到Boltzmann方程〜\ cite {suarxiv2019}的稳态解决方案，其中各种数值模拟已经表明（i）稳态解决方案可以在任何迭代范围内都可以在任何迭代率中找到稳定的元素，甚至在较大的范围内，即分子平均自由路径，即在粗网格下回收Navier-Stokes溶液。第一个属性表明，两次连续迭代之间的误差率在$ k $的情况下降至零，而第二个迭代率表示GSIS是渐近地保留Navier-Stokes限制的。本文致力于两种属性的严格证明。
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.
