TY - JOUR
T1 - General Synthetic Iterative Scheme for Unsteady Rarefied Gas Flows
AU - Zeng , Jianan
AU - Su , Wei
AU - Wu , Lei
JO - Communications in Computational Physics
VL - 1
SP - 173
EP - 207
PY - 2023
DA - 2023/08
SN - 34
DO - http://doi.org/10.4208/cicp.OA-2023-0068
UR - https://global-sci.org/intro/article_detail/cicp/21884.html
KW - Unsteady rarefied gas flow, general synthetic iterative scheme, fast convergence, asymptotic Navier-Stokes preserving.
AB - <p style="text-align: justify;">In rarefied gas flows, the spatial grid size could vary by several orders of
magnitude in a single flow configuration (e.g., inside the Knudsen layer it is at the
order of mean free path of gas molecules, while in the bulk region it is at a much
larger hydrodynamic scale). Therefore, efficient implicit numerical method is urgently
needed for time-dependent problems. However, the integro-differential nature of gas
kinetic equations poses a grand challenge, as the gain part of the collision operator
is non-invertible. Hence an iterative solver is required in each time step, which usually takes a lot of iterations in the (near) continuum flow regime where the Knudsen
number is small; worse still, the solution does not asymptotically preserve the fluid
dynamic limit when the spatial cell size is not refined enough. Based on the general
synthetic iteration scheme for steady-state solution of the Boltzmann equation, we propose two numerical schemes to push the multiscale simulation of unsteady rarefied
gas flows to a new boundary, that is, the numerical solution not only converges within
dozens of iterations in each time step, but also asymptotically preserves the Navier-Stokes-Fourier limit in the continuum flow regime, when the spatial grid is coarse, and
the time step is large (e.g., in simulating the extreme slow decay of two-dimensional
Taylor vortex, the time step is even at the order of vortex decay time). The properties
of fast convergence and asymptotic preserving of the proposed schemes are not only
rigorously proven by the Fourier stability analysis for simplified gas kinetic models,
but also demonstrated by several numerical examples for the gas kinetic models and
the Boltzmann equation.</p>