TY - JOUR
T1 - Fast convergence and asymptotic preserving of the general synthetic iterative scheme
AU - Su, Wei
AU - Zhu, Lianhua
AU - Wu, Lei
N1 - First published in SIAM Journal on Scientific Computing in Vol. 42 Issue 6, published by the Society for Industrial and Applied Mathematics (SIAM)
PY - 2020/12/14
Y1 - 2020/12/14
N2 - 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.
AB - 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.
KW - asymptotic Navier-Stokes preserving
KW - false/superconvergence
KW - gas kinetic equation
UR - http://www.scopus.com/inward/record.url?scp=85096225015&partnerID=8YFLogxK
UR - https://arxiv.org/abs/2003.09958
U2 - 10.1137/20M132691X
DO - 10.1137/20M132691X
M3 - Article
AN - SCOPUS:85096225015
SN - 1064-8275
VL - 42
SP - B1517-B1540
JO - SIAM Journal on Scientific Computing
JF - SIAM Journal on Scientific Computing
IS - 6
ER -