A kinetic Fokker–Planck approach to model hard-sphere gas mixtures

Hepp, Christian; Grabe, Martin; Hannemann, Klaus

doi:10.1063/1.5141909

Cited by 10 publications

(1 citation statement)

References 38 publications

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“…Other FP models, which satisfy the H-theorem and enable the adjustment of gas Prandtl number, include the modified streaming model 36,37 proposed by Singh and Ansumali 36 as well as the ellipsoidal statistical Fokker-Planck (ES-FP) model due to Mathiaud and Mieussens. 38 Extensions of FP models to multi-species gas mixtures were explored by Gorji and Jenny, 39 Agrawal et al, 40 and Hepp et al 41,42 Besides, various FP models for diatomic and polyatomic gases were constructed by Gorji and Jenny, 43 Mathiaud and Mieussens, 44,45 and Hepp et al 46 Recently, Fokker-Planck-type kinetic modeling for nonequilibrium dense gas and multi-phase flows were investigated by Sadr and Gorji 47 and Sadr et al 48 In addition to these theoretical modeling works, numerical issues related to the particle Fokker-Planck simulation (also referred to as Langevin dynamics simulation) and its applications have been attracting great interests. Gorji and Jenny 49 modified the original FP algorithm in Refs.…”

Section: Introductionmentioning

confidence: 99%

On the conservative property of particle-based Fokker–Planck method for rarefied gas flows

Jiang

Wen

2020

Physics of Fluids

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The Fokker-Planck-type approximation of the full Boltzmann equation has aroused intense research interest due to its potential for the stochastic particle simulation of rarefied gas flows. The ellipsoidal statistical Fokker-Planck (ES-FP) model treats the evolution of molecular velocity as a continuous stochastic process, and it satisfies the basic requirements for a proper gas-kinetic model including the H-theorem and an adjustable Prandtl number. The ES-FP model can be numerically implemented with computational particles in a Monte Carlo manner. Two different particle ES-FP schemes are presented. The first scheme utilizes the exact stochastic integral solution of the Langevin equations corresponding to the ES-FP equation and couples free-molecular moves and intermolecular collisions. The second scheme is designed to enforce the conservation of momentum and energy during the numerical simulation based on the decoupled algorithm and the analysis of the specific conditions for the conservative property. Numerical tests are conducted to demonstrate the performances of different schemes. In the simulation of a homogeneous gas system, the ES-FP scheme without enforcement of conservation leads to unphysical variation in the momentum and loss in energy, whereas the conservative ES-FP scheme strictly maintains the momentum and energy of the system. For the Mach 6 flows over the leading edge of a flat plate and over a round-nosed blunt body, the non-conservative ES-FP scheme underestimates the shock angle and the shock standoff distance, makes inaccurate predictions of aerodynamic force and heating, and produces low-temperature anomalies in front of the shock waves. In comparison with the results given by the direct simulation Monte Carlo method, the results of the conservative ES-FP simulations show satisfactory accuracy for the flow fields as well as the distributions of pressure, friction, and heat flux on the wall surfaces.

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