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This paper presents uniGasFoam, an open-source particle-based solver for multiscale rarefied gas flow simulations, which has been developed within the well-established OpenFOAM framework, and is an extension of the direct simulation Monte Carlo (DSMC) solver dsmcFoam+. The developed solver addresses the coupling challenges inherent in hybrid continuum-particle methods, originating from the disparate nature of finite-volume (FV) solvers found in computational fluid dynamics (CFD) software and DSMC particle solvers. This is achieved by employing alternative stochastic particle methods, resembling DSMC, to tackle the continuum limit. The uniGasFoam particle-particle coupling produces a numerical implementation that is simpler and more robust, faster in many steady-state flows, and more scalable for transient flows compared to conventional continuum-particle coupling. The presented framework is unified and generic, and can couple DSMC with stochastic particle (SP) and unified stochastic particle (USP) methods, or be employed for pure DSMC, SP, and USP gas simulations. To enhance user experience, optimise computational resources and minimise user error, advanced adaptive algorithms such as transient adaptive sub-cells, non-uniform cell weighting, and adaptive global time stepping have been integrated into uniGasFoam. In this paper, the hybrid USP-DSMC module of uniGasFoam is rigorously validated through multiple benchmark cases, consistently showing excellent agreement with pure DSMC, hybrid CFD-DSMC, and literature results. Notably, uniGasFoam achieves significant computational gains compared to pure dsmcFoam+ simulations, rendering it a robust computational tool well-suited for addressing multiscale rarefied gas flows of engineering importance.

Continuum fluid dynamic models based on the Navier-Stokes equations have previously been used to simulate granular media undergoing fluid-like shearing. These models, however, typically fail to predict the flow behaviour in confined environments as non-equilibrium particle effects dominate near walls. We adapt an extended hydrodynamic model for granular flows, which uses a density-gradient dependent ``volume diffusion'' term to correct the viscous stress tensor and heat flux, to simulate the shearing of a granular gas between two rough walls, and with corresponding boundary conditions. We use our volume diffusion model to predict channel flows for a range of mean volume fraction $\bar{\phi}=0.01$--$0.4$, and inter-particle coefficients of restitution $e=0.8$ and $0.9$, and compare with Discrete Element Method (DEM) simulations and classical Navier-Stokes equations. Our model is capable of predicting non-uniform pressure, volume fraction and granular temperature, which become more significant for cases with mean volume fraction $\bar{\phi}\sim0.1$, in which we typically observe non-uniform peak density variations, and large volume fraction gradients.

A new Micro-Macro-Surrogate (MMS) hybrid method is presented that couples the Direct Simulation Monte Carlo (DSMC) method with Computational Fluid Dynamics (CFD) to simulate low-speed rarefied gas flows. The proposed MMS method incorporates surrogate modelling instead of direct coupling of DSMC data with the CFD, addressing the limitations CFD has in accurately modelling rarefied gas flows, the computational cost of DSMC for low-speed and multiscale flows, as well as the pitfalls of noise in conventional direct coupling approaches. The surrogate models, trained on the DSMC data using Bayesian inference, provide noise-free and accurate corrections to the CFD simulation enabling it to capture the non-continuum physics. The MMS hybrid approach is validated by simulating low-speed, force-driven rarefied gas flows in a canonical parallel-plate system and shows excellent agreement with DSMC benchmark results. A comparison with the typical domain decomposition DSMC-CFD hybrid method is also presented, to demonstrate the advantages of noise-avoidance in the proposed approach. The method also inherently captures the uncertainty arising from micro-model fluctuations, allowing for the quantification of noise-related uncertainty in the predictions. The proposed MMS method demonstrates the potential to enable multiscale simulations where CFD is inaccurate and DSMC is prohibitively expensive.

Classical Navier-Stokes equations fail to describe some flows in both the compressible and incompressible configurations. In this article, we propose a new methodology based on transforming the fluid mass velocity vector field to obtain a new class of continuum models. We uncover a class of continuum models which we call the re-casted Navier-Stokes. They naturally exhibit the physics of previously proposed models by different authors to substitute the original Navier-Stokes equations. The new models unlike the conventional Navier-Stokes appear as more complete forms of mass diffusion type continuum flow equations. They also form systematically a class of thermo-mechanically consistent hydrodynamic equations via the original equations. The plane wave analysis is performed to check their linear stability under small perturbations, which confirms that all re-casted models are spatially and temporally stable like their classical counterpart. We then use the Rayleigh-Brillouin scattering experiments to demonstrate that the re-casted equations may be better suited for explaining some of the experimental data where original Navier-Stokes fail.