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) was proposed for the Boltzmann equation [W. Su et al., J. Comput. Phys., 407 (2020), 109245], 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., the Navier-Stokes solutions are recovered at coarse grids. The first property indicates that the error decay rate between two consecutive iterations decreases to zero along with K, while the second one implies that the GSIS asymptotically preserves the Navier-Stokes limit when K approaches zero. This paper is first dedicated to the rigorous proof of both properties. Second, several numerically challenging cases (especially the two-dimensional thermal edge flow) are used to further demonstrate the accuracy and efficiency of GSIS.

Original languageEnglish
Pages (from-to)B1517-B1540
Number of pages24
JournalSIAM Journal on Scientific Computing
Volume42
Issue number6
DOIs
Publication statusPublished - 14 Dec 2020

Keywords

  • asymptotic Navier-Stokes preserving
  • false/superconvergence
  • gas kinetic equation

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