Further acceleration of multiscale simulation of rarefied gas flow via a generalized boundary treatment

TL;DR

This paper introduces a generalized boundary treatment (GBT) to enhance the convergence speed of the generalized synthetic iterative scheme (GSIS) for simulating multiscale rarefied gas flows, achieving significant efficiency improvements.

Contribution

The paper proposes a novel GBT that reconstructs boundary conditions using macroscopic quantities and high-order corrections, accelerating GSIS convergence for complex gas flow simulations.

Findings

GSIS-GBT converges faster than previous methods in near-continuum and slip regimes.

GSIS-GBT achieves 10- to 100-fold speedup over traditional schemes.

The method maintains boundary accuracy validated by multiple simulation techniques.

Abstract

The recently-developed general synthetic iterative scheme (GSIS) is efficient in simulating multiscale rarefied gas flows due to the coupling of mesoscopic kinetic equation and macroscopic synthetic equation: for linearized Poiseuille flow where the boundary flux is fixed at each iterative step, the steady-state solutions are found within dozens of iterations in solving the gas kinetic equations, while for general nonlinear flows the iteration number is increased by about one order of magnitude, caused by the incompatible treatment of the boundary flux for the macroscopic synthetic equation. In this paper, we propose a generalized boundary treatment (GBT) to further accelerate the convergence of GSIS. The main idea is, the truncated velocity distribution function at the boundary, similar to that used in the Grad 13-moment equation, is reconstructed by the macroscopic conserved quantities from the synthetic equation, and the high-order correction of non-equilibrium stress and heat flux from the kinetic equation; therefore, in each inner iteration solving the synthetic equation, the explicit constitutive relations facilitate real-time updates of the macroscopic boundary flux, driving faster information exchange in the flow field, and consequently achieving quicker convergence. Moreover, the high-order correction derived from the kinetic equation can compensate the approximation by the truncation and ensure the boundary accuracy. The accuracy of GSIS-GBT is validated by the direct simulation Monte Carlo method, the previous versions of GSIS, and the unified gas-kinetic wave-particle method. For the efficiency, in the near-continuum flow regime and slip regime, GSIS-GBT can be faster than the conventional iteration scheme in the discrete velocity method and the previous versions of GSIS by two- and one-order of magnitude, respectively.