Fast convergence and asymptotic preserving of the general synthetic iterative scheme

Su，Wei1; Zhu，Lianhua2; Wu，Lei3

2020-12-01

10.1137/20M132691X

SIAM JOURNAL ON SCIENTIFIC COMPUTING   影响因子和分区

1064-8275

1095-7197

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.

Asymptotic Navier-Stokes preserving False/superconvergence Gas kinetic equation

SCI ; EI

英语

其他

WOS:000600650400032

20210209754887

Boltzmann equation ; Decay (organic)

Biochemistry:801.2 ; Calculus:921.2 ; Statistical Methods:922

MATHEMATICS

2-s2.0-85096225015

Scopus

1.School of Engineering,University of Edinburgh,Edinburgh,EH9 3FB,United Kingdom
2.James Weir Fluids Laboratory,Department of Mechanical and Aerospace Engineering,University of Strathclyde,Glasgow,G1 1XJ,United Kingdom
3.Department of Mechanics and Aerospace Engineering,Southern University of Science and Technology,Shenzhen,518055,China

Su，Wei,Zhu，Lianhua,Wu，Lei. Fast convergence and asymptotic preserving of the general synthetic iterative scheme[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2020,42(6):B1517-B1540.

Su，Wei,Zhu，Lianhua,&Wu，Lei.(2020).Fast convergence and asymptotic preserving of the general synthetic iterative scheme.SIAM JOURNAL ON SCIENTIFIC COMPUTING,42(6),B1517-B1540.

Su，Wei,et al."Fast convergence and asymptotic preserving of the general synthetic iterative scheme".SIAM JOURNAL ON SCIENTIFIC COMPUTING 42.6(2020):B1517-B1540.