Fluid Simulations with Localized Boltzmann Upscaling by Direct Simulation Monte-Carlo

In the present work, we present a novel numerical algorithm to couple the Direct Simulation Monte Carlo method (DSMC) for the solution of the Boltzmann equation with a finite volume like method for the solution of the Euler equations. Recently we presented in [14],[16],[17] different methodologies which permit to solve fluid dynamics problems with localized regions of departure from thermodynamical equilibrium. The methods rely on the introduction of buffer zones which realize a smooth transition between the kinetic and the fluid regions. In this paper we extend the idea of buffer zones and dynamic coupling to the case of the Monte Carlo methods. To facilitate the coupling and avoid the onset of spurious oscillations in the fluid regions which are consequences of the coupling with a stochastic numerical scheme, we use a new technique which permits to reduce the variance of the particle methods [11]. In addition, the use of this method permits to obtain estimations of the breakdowns of the fluid models less affected by fluctuations and consequently to reduce the kinetic regions and optimize the coupling. In the last part of the paper several numerical examples are presented to validate the method and measure its computational performances.

💡 Research Summary

The paper introduces a novel multiscale algorithm that couples the Direct Simulation Monte Carlo (DSMC) method for solving the Boltzmann equation with a finite‑volume (FV) discretization of the Euler equations. The motivation stems from the well‑known difficulty of handling flows that are mostly in thermodynamic equilibrium but contain localized regions where kinetic effects dominate. Traditional approaches either apply a kinetic solver everywhere—incurring prohibitive computational cost—or rely solely on a fluid solver, which fails to capture non‑equilibrium phenomena. The authors build on their earlier work (references