A high-order Monte Carlo algorithm for the direct simulation of Boltzmann equation

Jahangiri, Pouyan; Nejat, Amir; Samadi, Jila; Aboutalebi, Ali

doi:10.1016/j.jcp.2012.02.029

Cited by 6 publications

(2 citation statements)

References 11 publications

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“…Q ≡ 0) (3) and the equation of collision step (i.e. υ · ∇x ≡ 0) (4) (Bird 1994;Pareschi and Trazzi 2005;Pareschi and Caflisch 1999;Trazzi, Pareschi, and Wennberg 2009;Jahangiri, Nejat, Samadi, and Aboutalebi 2012;Yanenko 1971).…”

Section: Boltzmann Equationmentioning

confidence: 99%

On the Expedient Solution of the Boltzmann Equation by Modified Time Relaxed Monte Carlo (MTRMC) Method

Eskandari

Nourazar

2018

JAFM

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In the present study, a modified time relaxed Monte Carlo (MTRMC) method is developed for numerical solution of the Boltzmann equation in rarefied regimes. Taylor series expansion is employed to obtain a generalized form of the Wild sum expansion and consequently the modified collision functions with fewer inter-molecular interactions are obtained. The proposed algorithm is applied on the lid-driven micro cavity flow with different lid velocities and the results for velocity and shear stress distributions are compared with those from the standard DSMC and TRMC methods. The comparisons show excellent agreement between the results of the MTRMC method with their counterparts from TRMC and DSMC methods. The present study illustrates appreciable improvement in the computational expense of the MTRMC method compared to those from standard TRMC and DSMC methods. The improvement is more pronounced compared to the standard DSMC method. It is observed that up to 56% reduction in CPU time is obtained in the studied cases.

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Section: Boltzmann Equationmentioning

confidence: 99%

On the Expedient Solution of the Boltzmann Equation by Modified Time Relaxed Monte Carlo (MTRMC) Method

Eskandari

Nourazar

2018

JAFM

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“…The original DSMC has first-order accuracy due to the decoupling treatment of convection and collision terms. The higher-order DSMC method was constructed by improving the temporal accuracy of the collision term [11]. However, statistical noise from particle method is still not resolved to get accurate solution.…”

Section: Introductionmentioning

confidence: 99%

High-order Unified Gas-kinetic Scheme

Lim¹,

Zhu²,

Xu³

2022

Preprint

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In this paper, we present a high-order unified gas-kinetic scheme (UGKS) using the weighted essentially non-oscillatory with adaptive-order (WENO-AO) method for spatial reconstruction and the two-stage fourth-order scheme for time evolution. Since the UGKS updates both the macroscopic flow variables and microscopic distribution function, and provides an adaptive flux function by combining the equilibrium and non-equilibrium parts, it is possible to take separate treatment of the equilibrium and non-equilibrium calculation in the UGKS for the development of high-order scheme. Considering the fact that high-order techniques are commonly required for continuum flow with complex structures, and the rarefied flow structure are relatively simple and smooth in the physical space, we apply the highorder techniques in the equilibrium part of the UGKS for the capturing of macroscopic flow evolution, and retain the calculation of distribution function as a second-order method, so that a balance of computational cost and numerical accuracy could be well achieved. The high-order UGKS has been validated by several numerical test cases, including sine-wave accuracy test, sod-shock tube, Couette, oscillating Couette, lid-driven cavity and oscillating cavity flow. It is shown that the current method preserves the multiscale property of the original UGKS and obtains more accurate solutions in several cases.

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Bifurcation, chaos, and their control in a wheelset model

Cui

2020

Math Methods in App Sciences

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In this paper, we present an improved wheelset motion model with two degrees of freedom and study the dynamic behaviors of the system including the symmetry, the existence and uniqueness of the solution, continuous dependence on initial conditions, and Hopf bifurcation. The dynamic characteristics of the wheelset motion system under a nonholonomic constraint are investigated. These results generalize and improve some known results about the wheelset motion system. Meanwhile, based on multiple equilibrium analysis, calculation of Lyapunov exponents and Poincaré section, the chaotic behaviors of the wheelset system are discussed, which indicates that there are more complex dynamic behaviors in the railway wheelset system with higher order terms of Taylor series of trigonometric functions. This paper has also realized the chaos control and bifurcation control for the wheelset motion system by adaptive feedback control method and linear feedback control. The results show that the chaotic wheelset system and bifurcation wheelset system are all well controlled, whether by controlling the yaw angle and the lateral displacement or only by controlling the yaw angle. Numerical simulations are carried out to further verify theoretical analyses.

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A high-order Monte Carlo algorithm for the direct simulation of Boltzmann equation

Cited by 6 publications

References 11 publications

On the Expedient Solution of the Boltzmann Equation by Modified Time Relaxed Monte Carlo (MTRMC) Method

On the Expedient Solution of the Boltzmann Equation by Modified Time Relaxed Monte Carlo (MTRMC) Method

High-order Unified Gas-kinetic Scheme

Bifurcation, chaos, and their control in a wheelset model

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