A Hybrid CFD-DSMC Method of Modeling Continuum-Rarefied Flows

Abstract

A hybrid method of simulating high-speed, non-equilibrium flows solves the Navier-Stokes equations using a Computational Fluid Dynamics (CFD) model in regions of the flow where properties are continuous and a statistical Direct Simulation Monte Carlo (DSMC) model in regions where properties are non-continuous and thermal nonequilibrium exists. The hybrid method is designed to balance computational efficiency and accuracy by utilizing a relatively inexpensive CFD model whenever appropriate and the DSMC model in critical regions of thermal non-equilibrium. The algorithm uses locally computed values of a breakdown parameter to evaluate the continuum assumption and turns on the DSMC component when the parameter exceeds a threshold value. The DSMC algorithm utilizes the methods of Information Preservation (IP) and ghost cells to accurately and efficiently exchange macroscopic flow properties with the CFD algorithm.Comparisons are made between experimental data for argon flow in a shock tube at Mach numbers 1.55, 5.0, and 10.0 using three computational models-pure CFD, pure DSMC, and hybrid CFD-DSMC. At Mach 1.55, close agreement exists between the experimental data and all of the computational models. At Mach 5 and 10, non-equilibrium becomes significant through the shock layer, and the CFD results diverge from the experimental data. Close agreement exists between the experimental data and both the DSMC and the hybrid simulations at all three Mach numbers, demonstrating that the hybrid method accurately models both equilibrium and non-equilibrium flows. Currently, the hybrid model is more, rather than less, expensive than the pure DSMC model-as a result of limits on the maximum allowable time step size imposed by the IP algorithm. A primary objective of future work is to significantly reduce the computational expense of the hybrid method by incorporating a more robust IP formulation.

Progress in particle-based multiscale and hybrid methods for flow applications

“…A pure Navier-Stokes solution was also tested which gave inaccurate results with the reciprocal shock thickness overestimated by almost a factor of 2. This is consistent with the observation of Carlson et al (2004), who computed the flow inside a shock tube for Mach numbers of 1.55, 5 and 10. In their multiscale solver, the Navier-Stokes equations were coupled with the DSMC method based on the IP method (information preserving, Fan and Shen 2001).…”

Unified solver for rarefied and continuum flows with adaptive mesh and algorithm refinement

“…An adaptive mesh and algorithm refinement (AMAR) procedure has been developed for a DSMC-based particle method to supplement the grid refinement by algorithm refinement (continuum vs atomistic) based on continuum breakdown criteria [16]. However, statistical noise inherent to DSMC has been identified as an obstacle for the development of hybrid solvers [17,18]. Due to strong fluctuations of the macroparameters calculated from the DSMC, the problem of connecting kinetic and continuum regions is complicated by severe stability problems when DSMC data is handed over to a continuum solver at the interface.…”

“…The first category includes methods employing domain decomposition in physical space. In this category, the computational domain is decomposed into kinetic and continuum sub-domains using appropriate criteria [3][4][5][6][7][8][9][10][11][12]. The second category includes methods based on domain decomposition in velocity space where fast and slow particles are treated separately [13].…”

Coupling Atomistic and Continuum Models for Multi-scale Simulations of Gas Flows

“…Particle methods such as DSMC or Molecular Dynamics are used in regions with strong deviations from equilibrium, and continuum (Euler or NS) solvers are used elsewhere. Statistical noise inherent to DSMC has been identified as an obstacle for the development of hybrid solvers [5]. Direct methods of solving Boltzmann equation have recently emerged as a viable alternative to the particle methods [6][7][8].…”