arXiv subjects

Joonbeom Kim

Publications and source records attributed to Joonbeom Kim.

3 recordsLinked to original sources

arXiv2026

A Particle Multi-Relaxation Bhatnagar-Gross-Krook Method for Rarefied Monatomic Gas Mixtures

Kinetic models based on the Bhatnagar-Gross-Krook (BGK) framework provide an efficient alternative to the Boltzmann equation for rarefied gas flows; however, existing formulations for gas mixtures remain limited in representing pair-dependent relaxation processes and recovering correct Navier-Stokes-Fourier (NSF) transport behavior. A particle-based unified BGK (UBGK) model for monatomic gas mixtures is developed by extending the single-species UBGK framework to a multi-relaxation formulation. The model preserves the pairwise interaction structure of the mixture Boltzmann equation, enabling independent species-pair relaxations for an arbitrary number of species. The relaxation properties of the mixture UBGK model are determined by matching the production terms to those of the Boltzmann equation, ensuring correct NSF-level transport behavior. The model is implemented within the particle framework and validated against DSMC using four benchmark cases: homogeneous relaxation, Poiseuille flow, Couette flow, and hypersonic flow around a cylinder. The results demonstrate that the mixture UBGK model captures species-specific non-equilibrium effects, including species-dependent differences in velocity and temperature, across a range of mole fractions and Knudsen numbers in good agreement with DSMC. Furthermore, cost and accuracy analyses show that the mixture UBGK model becomes more efficient than DSMC at sufficiently large time step sizes, but its first-order accuracy suggests further improvement through higher-order schemes.

physics.flu-dyn↗

arXiv2025

A second-order particle Fokker-Planck-Master method for diatomic gas flows

The direct simulation Monte Carlo (DSMC) method is widely used to describe rarefied gas flows. The DSMC method accounts for the transport and collisions of computational particles, resulting in higher computational costs in the continuum regime. The Fokker-Planck (FP) model approximates particle collisions as Brownian motion to reduce computational cost. Advanced FP models have been developed to enhance physical fidelity, ensuring the correct Prandtl number and the H-theorem. The FP model has further been extended to handle diatomic gases, such as the Fokker-Planck-Master (FPM) model. Alongside these developments in modeling, computational efficiency has also been improved by achieving second-order spatial and temporal accuracy, as demonstrated in the unified stochastic particle FP (USP-FP) method. However, these accuracy improvements have not yet been extended to diatomic gases, which are essential for engineering applications such as atmospheric reentry. This study proposes a unified stochastic particle Fokker-Planck-Master (USP-FPM) method for diatomic gases that achieves second-order accuracy in both time and space. Temporal accuracy is enhanced by reproducing second-order energy, viscous stress, and heat flux relaxations. Spatial accuracy is improved by employing a first-order polynomial reconstruction method. Three test cases are investigated: homogeneous relaxation, Poiseuille flow, and hypersonic flow around a cylinder. The results show that the USP-FPM method provides accurate solutions even with coarser cell sizes and larger time steps compared to the DSMC and FPM methods. In particular, for the hypersonic flow around a cylinder, the USP-FPM method achieves a speed-up factor of 28 compared to the DSMC method, while maintaining accuracy.

physics.comp-ph↗

arXiv2025

Improving Spatio-Temporal Accuracy of the Stochastic Particle Fokker-Planck Model

Accurate prediction of rarefied gas flows is important for space vehicle design, particularly in rarefied regimes where the Navier-Stokes equations are no more valid. While the direct simulation Monte Carlo (DSMC) method acts as a numerical solver for rarefied gas flows, it becomes inefficient when dealing with near-continuum regimes. The Fokker-Planck (FP) model improves computational efficiency by approximating particle collisions as a drift-diffusion process. The FP model has been extended to handle diatomic gases, such as the Fokker-Planck-Master (FPM) model. The FPM model's first-order accuracy in both time and space limits computational efficiency gains. This study proposes a unified stochastic particle FPM (USP-FPM) model that achieves second-order spatio-temporal accuracy for diatomic gases. Temporal accuracy is improved by introducing second-order energy relaxation into the USP-FP method. Spatial accuracy is improved by employing a polynomial reconstruction method for macroscopic properties. The USP-FPM model is validated through two numerical simulations: relaxation to thermal equilibrium in a homogeneous flow and hypersonic flow over a vertical plate. The results demonstrate that the USP-FPM model shows good agreement with DSMC results and significantly reduces computational cost by enabling larger cell sizes and time steps.

physics.flu-dyn↗