A hybrid numerical algorithm based on the stochastic particle Shakhov and DSMC method

TL;DR

This paper introduces a hybrid numerical algorithm combining the stochastic particle Shakhov model with DSMC to efficiently simulate multi-scale rarefied and continuum gas flows, addressing computational challenges in existing methods.

Contribution

A novel hybrid particle method coupling the stochastic particle Shakhov with DSMC based on local timescale decomposition, improving efficiency and accuracy in multi-scale gas flow simulations.

Findings

Validated with benchmark cases including shock tube and hypersonic flows.

Demonstrated improved computational efficiency over traditional DSMC.

Achieved accurate results in near-continuum and rarefied regimes.

Abstract

The Direct Simulation Monte Carlo (DSMC) method is widely employed for simulating rarefied nonequilibrium gas flows. With advances in aerospace engineering and micro/nano-scale technologies, gas flows exhibit the coexistence of rarefied and continuum/near-continuum regimes, which calls for larger time steps and coarser spatial grids for efficient numerical simulation. However, the mesh sizes and time steps in DSMC are constrained by the single-scale nature of the Boltzmann equation and the explicit treatment of collision term following operator splitting. To overcome the resulting computational inefficiency, the Time-Relaxed Monte Carlo (TRMC) method introduces a suitable time discretization of the Boltzmann equation, allowing for significantly larger time steps. Besides, domain decomposition methods leverage the complementary strengths of continuum and particle-based approaches, facilitating the efficient simulation of multi-scale gas flows. However, in TRMC method, the physically accurate high-order terms are truncated and approximated through convergence to a local Maxwellian distribution. Meanwhile, the continuum breakdown criteria employed in hybrid methods are either empirical or semi-empirical. Recently, a timescale-based decomposition of the Boltzmann equation has been proposed to enable a more rational coupling between DSMC and Navier-Stokes. Inspired by this strategy, a novel hybrid particle method is proposed to couple the stochastic particle Shakhov with DSMC, in which the collision operator is decomposed into two sub-steps based on local observation timescale and the relaxation time. The validity and accuracy of the proposed method are demonstrated through a series of benchmark cases, including 1-D sod shock tube, 2-D hypersonic flow around cylinder and jet expansion into the vacuum, 3-D hypersonic flows around sphere and X-38 like vehicle in near-continuum flow regimes.