Fast convergence and asymptotic preserving of the General Synthetic Iterative Scheme
arXiv:2003.09958
Abstract
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 , 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 , 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.
References in corpus (6)
- A class of asymptotic preserving schemes for kinetic equations and related problems with stiff sources
- A Unified Gas-kinetic Scheme for Continuum and Rarefied Flows IV: full Boltzmann and Model Equations
- Can we find steady-state solutions to multiscale rarefied gas flows within dozens of iterations?
- Comparative study of the discrete velocity and lattice Boltzmann methods for rarefied gas flows through irregular channels
- A fast iterative scheme for the linearized Boltzmann equation
- A high-order hybridizable discontinuous Galerkin method with fast convergence to steady-state solutions of the gas kinetic equation