Session A08: Rarefied Flows

Spectral Simulations of Fluid-Kinetic Flows with Nontrivial Boundary Conditions

We model flows in regimes where atomistic effects are important, but at scales where kinetic calculations are not possible, by using a unified discretization of the multispecies Boltzmann equation that is valid across near-continuum as well as kinetic-dominated regions. For simplicity, collisions are modeled with the Bhatnagar-Gross-Krook operator, although generalizations are straightforward. The highly dimensional phase space is made tractable with asymmetrically weighted Hermite basis functions providing a spectral representation of the velocity space, high order finite differences providing a conservative spatial discretization, and embedded Runge-Kutta methods providing an adaptive temporal discretization. Additional adaptivity is achieved by varying the number of terms in the spectral expansion as needed to capture the relevant physics. Because of our particular choice in basis functions, near-continuum regions require only the first few spectral coefficients, while regions with strong kinetic effects require more terms in the expansion. We demonstrate the physics capabilities on several canonical test cases, including with nontrivial boundary conditions, such as Maxwell's diffuse walls.   

Momentum and Energy Transport in rarefied cavity flow Across Compressibility and Knudsen Number Ranges

The present study investigates the energy and momentum transport of Argon (Ar) in a lid-driven cavity setup across a range of compressibility (0.16 < Ma < 3.0) and rarefaction (10^-4 < Kn < 10²) conditions. We explore the behavior in different flow regimes using the Gas Kinetic Scheme (GKS), which calculates fluxes based on higher-order moments of the distribution function, and the Unified Gas Kinetic Scheme (UGKS), which employs multiple equi-variant distribution functions and is applicable across the entire Knudsen spectrum. We define breakdown parameters to characterize the rarefaction regimes captured by both GKS and UGKS. Our study examines Fourier and anti-Fourier (co-gradient) heat transport, as well as the misalignment between the deviatoric stress tensor (derived from higher-order statistics of peculiar velocity) and the constitutive strain tensor. We also analyze pressure anisotropy in the compressible (Ma = 3) and highly rarefied (Kn ~10) regimes, noting that the maximum contribution arises in the direction of the external forcing, i.e., the lid velocity direction. Furthermore, we compare various slip velocity models with UGKS cases for both stationary and moving walls, assessing the degree of departure from equilibrium. This comprehensive examination provides deeper insights into the complex behavior of gases under varying flow conditions and enhances our understanding of kinetic schemes in predicting fluid behavior in non-equilibrium states.   

Experimental investigation of the interaction of a pair of supersonic jets in near vacuum

Semiconductor processes are traditionally carried out in rarefied gas environments due to various reasons including purity requirements, deposition efficiency, and plasma generation. Although the overall conditions are near vacuum, gas jets are utilized for various processes within vacuum process chambers. The jets that supply process gases are arranged in various configurations, such as showerhead arrays, to provide uniform flow. In single wafer process chambers, the jets are mostly located at the top of the chamber, with the distance to the wafer being more than 100 times the jet diameter. Therefore, it is necessary to understand the jet merging process and resulting far-field flow structure at near vacuum conditions. Previous studies have mainly focused on single jet shockwaves in the near field, with limited analysis of multi-jet merging in the far field. This study analyzes the merging of a pair of jets utilizing acetone molecular tagging velocimetry (MTV). The results will provide a baseline for further studies of multi-jets in near vacuum environments.   

Experimental investigation of the flow regimes in a rarefied supersonic free jet according to complex Reynolds number

Recent technological advancements necessitate an in-depth understanding of fluid dynamics in rarefied gas environments, vital for semiconductor and aerospace industries. Free jets used in semiconductor deposition and satellite control exhibit complex shockwave structures in these conditions, complicating understanding of the flow. Previous studies focused mainly on near-field shockwaves. However, understanding the far-field zone post-shockwave dissipation is crucial for vacuum applications. This study quantitatively visualizes 2D flow fields of supersonic circular free jets in rarefied conditions. We analyzed shockwave and flow structures in the near-field and far-field zones to establish a reliable experimental basis for vacuum environments. Using nanometer-sized particles for particle image velocimetry (PIV) and acetone for molecular tagging velocimetry (MTV), the study measured supersonic jet flows at 1 torr. A one-barrel shockwave in the near-field and a long annular viscous layer beyond the Mach disk was observed. The far-field zone transitioned to a laminar regime, matching theoretical predictions based on the complex Reynolds number. These findings provide essential experimental evidence for designing equipment for vacuum environments.   

A characteristic mapping method for high resolution simulations of plasma with collisions

We present first results towards simulating kinetic plasmas with collisions using the characteristic mapping method (CMM) [1]. CMM is a semi-Lagrangian method that utilises the semi-group structure of diffeomorphic flows. Here the flow map is decomposed into submaps that relate the flow backward in time to its initial point. This compositional refinement enables exponential resolution within linear time. In addition to [1] we extend CMM to handle source terms by storing sub-integrals corresponding to individual submaps, which facilitates efficient integration. Moreover, it exploits the Lagrangian structure to circumvent implicit time integration in the hydrodynamic regime, which is notoriously stiff. We will demonstrate the effectiveness of the CMM method by benchmarking it using BGK and Vlasov-Poisson-BGK equations.

[1] P. Krah, X.-Y. Yin, J. Bergmann, J.-C. Nave and K. Schneider. A Characteristic Mapping Method for Vlasov-Poisson with extreme resolution properties. Commun. Comput. Phys., 35(4):905-937, 2024   

Enabling general meso-scale ablation simulations via direct simulation Monte Carlo

Direct simulation Monte Carlo (DSMC) [1] is a stochastic particle method that can track individual gas-surface and gas-gas reactions, making it a prime candidate for simulating ablation at meso-scales. Recently, we have developed a surface conversion capability within Sandia’s direct simulation Monte Carlo solver, SPARTA [2] to allow DSMC ablation simulations of complex bodies. However, for the surface conversion to be robust, the vertices of the surface elements shift. Moreover, the simulated surface recession does not correctly match the expected local mass flux.  The combination of these two causes DSMC to augment the surface roughness which can mask cell-level features (which are on the scale of the mean free path) and disturb the nearby flow. Two modifications are made to the ablation framework: inner indices and multi-point cell decrement. The combination of the two enable more physically realistic DSMC ablation simulations.

[1] Bird, G. A. (1994). Molecular gas dynamics and the direct simulation of gas flows. Oxford university press.

[2] Plimpton, S. J., Moore, S. G., Borner, A., Stagg, A. K., Koehler, T. P., Torczynski, J. R., & Gallis, M. A. (2019). Direct simulation Monte Carlo on petaflop supercomputers and beyond. Physics of Fluids, 31(8).   

DSMC Performance Frontiers: Interplay of Physics and Computation

The Direct Simulation Monte Carlo (DSMC) method is a widely accepted technique for simulating rarefied gas flows, renowned for its high accuracy in capturing non-equilibrium phenomena. However, its significant computational costs often hinder its application to complex problems. This study aims to comprehensively evaluate the computational demands and performance of the DSMC method across various scenarios, with a focus on optimization strategies to improve its efficiency.

We investigate the multi-threading performance, revealing a non-linear dependence of simulation time on processor count. Our results show that increasing processor count reduces simulation time up to a threshold, beyond which a bottleneck effect emerges due to inter-thread communication overhead, limiting the efficiency of multi-threaded DSMC simulations. To further accelerate the DSMC method, we also explore the utilization of Graphical Processing Units (GPUs).

Furthermore, we examine the impact of temperature, Knudsen number, and the corresponding Maxwell-Boltzmann distribution on the performance of DSMC method. This systematic analysis provides valuable insights into optimizing DSMC simulations for diverse physical conditions, including low-speed and high-speed flows, and sheds light on the complex interplay between computational efficiency and physical accuracy.