arXiv subjects

Félix Garmirian

Publications and source records attributed to Félix Garmirian.

4 recordsLinked to original sources

arXiv2026

Implementation and Extension of the Variance-Reduced BGK Method in PICLas

Traditional particle-based kinetic methods, such as DSMC, suffer from prohibitive computational cost in low-signal flows, where the deviation from thermodynamic equilibrium is small and statistical noise overwhelms the signal of interest. The Variance-Reduced BGK-DSMC scheme is further advanced and implemented to support this class of flows in the open-source gas-kinetics framework PICLas. Modified versions of flow estimators and collision operators enhancing stability are developed. The Shakhov and Ellipsoidal Statistical models for BGK are demonstrated, along with entirely new features such as adaptive equilibria, variable particle weights and domain axisymmetry. The implementation is validated using synthetic benchmarks, 1D, 2D and axisymmetric simulations. Comparison of VRBGK to BGK simulations shows exact agreement of the models. A further comparison with an analytical solution of thermal transpiration in a microchannel showcases the low-signal efficiency of the method as well as newly proposed features.

physics.flu-dyn↗

arXiv2025

Implementation of Asymptotic Preserving Discrete Velocity Methods into the Simulation Code PICLas

The Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation allows for efficient flow simulations, especially in the transition regime between continuum and high rarefaction. However, ensuring efficient performances for multiscale flows, in which the Knudsen number varies by several orders of magnitude, is never straightforward. Discrete velocity methods as well as particle-based solvers can each reveal advantageous in different conditions, but not without compromises in specific regimes. This article presents a second-order asymptotic preserving discrete velocity method to solve the BGK equation, with the particularity of maintaining positivity when operations are conducted with the cell-local distribution function. With this procedure based on exponential differencing, it is therefore also possible to construct an adapted version of this second-order method using the stochastic particle approach, as previously presented. The deterministic variant and its implementation are detailed here and its performances are evaluated on several test cases. Combined to the probabilistic solver and with the possibility of a future coupling, our exponential differencing discrete velocity method provides a robust toolbox, useful for efficiently simulating multiscale gas phenomena.

physics.flu-dyn↗

arXiv2024

Crank-Nicolson BGK Integrator for Multi-Scale Particle-Based Kinetic Simulations

Solving the Bhatnagar-Gross-Krook (BGK) equation with a stochastic particle approach enables efficient and flexible simulations of flows in the transition regime, between continuum and free molecular flow. However, the usual first-order operator splitting between particle movement and relaxation imposes restrictions on the time step, causing the computational cost to increase with the gas density. The Crank-Nicolson stochastic particle BGK (CN-SPBGK) method is introduced here as an advanced particle-based kinetic solver designed for multi-scale gas flow simulations. This method integrates the BGK equation with second-order accuracy across all Knudsen number regimes without requiring additional parameters, while asymptotically preserving the Navier-Stokes flux in the continuum regime. Comparisons with pre-existing particle BGK methods are conducted on several test cases, with CN-SPBGK demonstrating more consistent convergence and accuracy.

physics.flu-dyn↗

arXiv2022

Exponential BGK Integrator for Multi-Scale Particle-Based Kinetic Simulations

Despite the development of an extensive toolbox of multi-scale rarefied flow simulators, such simulations remain challenging due to the significant disparity of collisional and macroscopic spatio-temporal scales. Our study offers a novel and consistent numerical scheme for a coupled treatment of particles advection and collision governed by the BGK evolution, honouring positivity of the velocity distribution. Our method shares its framework, in spirit, with the unified gas kinetic class of multi-scale schemes. Yet it provides attractive features for particle-based stochastic simulations, readily implementable to existing direct simulation Monte-Carlo codes. We demonstrate accuracy and performance of the devised scheme for prototypic gas flows, over a wide-range of rarefaction parameters. Due to the resulting robustness and flexibility of the devised exponential BGK integrator, the scheme paves the way towards more affordable simulations of large- and multi-scale rarefied gas phenomena.

physics.flu-dyn↗