An efficient treatment of heat-flux boundary conditions in GSIS for rarefied gas flows

TL;DR

This paper introduces an efficient boundary condition treatment in GSIS for rarefied gas flows, reducing iterations and improving convergence while maintaining accuracy, demonstrated through various 3D and 2D simulations.

Contribution

It proposes a novel boundary flux estimation method within GSIS that enhances efficiency and convergence in simulating rarefied gas flows.

Findings

Significant reduction in iteration count for boundary parameter determination.

Good agreement with DSMC results in complex flow configurations.

Enhanced efficiency over traditional iterative schemes.

Abstract

Heat-flux boundary conditions are challenging to implement efficiently in rarefied gas flow simulations because the wall-reflected gas temperature and density must be determined dynamically during the computation. This paper aims to tackle this problem within the general synthetic iterative scheme (GSIS), where the Boltzmann kinetic equation is solved deterministically in an outer loop and macroscopic synthetic equations are solved in an inner loop. To avoid kinetic-macroscopic boundary-flux mismatch and the resulting convergence bottlenecks, for the macroscopic boundary flux at every inner iteration, the incident increment is estimated using a Maxwellian distribution, and then the reflected contribution is obtained by boundary conditions consistent with those in the kinetic solver. In addition to retaining the fast-converging and asymptotic-preserving properties of GSIS, the proposed method significantly reduces the iterations required to determine the wall-reflected gas parameters. Numerical simulations of rarefied gas flows in and around a 3D nozzle, a 2D adiabatic cylinder, and a 2D annular heat-transfer configuration show good agreement with the direct simulation Monte Carlo method, while achieving substantial efficiency gains over conventional iterative schemes.