Boosting the convergence of low-variance DSMC by GSIS

Luo, Liyan; Li, Qi; Wu, Lei

2023-03-03

10.1186/s42774-023-00138-0

ADVANCES IN AERODYNAMICS   Impact Factor & Quartile

2524-6992

The low-variance direct simulation Monte Carlo (LVDSMC) is a powerful method to simulate low-speed rarefied gas flows. However, in the near-continuum flow regime, due to limitations on the time step and spatial cell size, it takes plenty of time to find the steady-state solution. Here we remove these deficiencies by coupling the LVDSMC with the general synthetic iterative scheme (GSIS) which permits the simulation at the hydrodynamic scale rather than the much smaller kinetic scale. As a proof of concept, we propose the stochastic-deterministic coupling method based on the Bhatnagar-Gross-Krook kinetic model. First, macroscopic synthetic equations are derived exactly from the kinetic equation, which not only contain the Navier-Stokes-Fourier constitutive relation, but also encompass the higher-order terms describing the rarefaction effects. Then, the high-order terms are extracted from LVDSMC and fed into synthetic equations to predict the macroscopic properties which are closer to the steady-state solution than LVDSMC. Finally, the state of simulation particles in LVDSMC is updated to reflect the change of macroscopic properties. As a result, the convergence to steady state is greatly accelerated, and the restrictions on cell size and the time step are removed. We conduct the Fourier stability analysis and simulate several canonical rarefied gas flows to demonstrate the advantages of LVDSMC-GSIS: when the Knudsen number is lower than 0.1, it can use the grid size about 10 times larger than that in traditional DSMC, and it can reduce the computational cost by two orders of magnitude in the flow regime.

Rarefied gas dynamics Direct simulation Monte Carlo General synthetic iterative scheme Multiscale simulation

ESCI

English

First ; Corresponding

Engineering ; Mechanics ; Physics

Engineering, Mechanical ; Mechanics ; Physics, Fluids & Plasmas

WOS:000943141400001

SPRINGERNATURE

2-s2.0-85149514838

Web of Science

Southern Univ Sci & Technol, Dept Mech & Aerosp Engn, Shenzhen 518055, Peoples R China

Luo, Liyan,Li, Qi,Wu, Lei. Boosting the convergence of low-variance DSMC by GSIS[J]. ADVANCES IN AERODYNAMICS,2023,5(1).

Luo, Liyan,Li, Qi,&Wu, Lei.(2023).Boosting the convergence of low-variance DSMC by GSIS.ADVANCES IN AERODYNAMICS,5(1).

Luo, Liyan,et al."Boosting the convergence of low-variance DSMC by GSIS".ADVANCES IN AERODYNAMICS 5.1(2023).