Polar-coordinate lattice Boltzmann modeling of compressible flows

Chuandong Lin, Aiguo Xu, Guangcai Zhang, Yingjun Li, and Sauro Succi

Phys. Rev. E 89, 013307 – Published 21 January 2014

Abstract

We present a polar coordinate lattice Boltzmann kinetic model for compressible flows. A method to recover the continuum distribution function from the discrete distribution function is indicated. Within the model, a hybrid scheme being similar to, but different from, the operator splitting is proposed. The temporal evolution is calculated analytically, and the convection term is solved via a modified Warming-Beam (MWB) scheme. Within the MWB scheme a suitable switch function is introduced. The current model works not only for subsonic flows but also for supersonic flows. It is validated and verified via the following well-known benchmark tests: (i) the rotational flow, (ii) the stable shock tube problem, (iii) the Richtmyer-Meshkov (RM) instability, and (iv) the Kelvin-Helmholtz instability. As an original application, we studied the nonequilibrium characteristics of the system around three kinds of interfaces, the shock wave, the rarefaction wave, and the material interface, for two specific cases. In one of the two cases, the material interface is initially perturbed, and consequently the RM instability occurs. It is found that the macroscopic effects due to deviating from thermodynamic equilibrium around the material interface differ significantly from those around the mechanical interfaces. The initial perturbation at the material interface enhances the coupling of molecular motions in different degrees of freedom. The amplitude of deviation from thermodynamic equilibrium around the shock wave is much higher than those around the rarefaction wave and material interface. By comparing each component of the high-order moments and its value in equilibrium, we can draw qualitatively the main behavior of the actual distribution function. These results deepen our understanding of the mechanical and material interfaces from a more fundamental level, which is indicative for constructing macroscopic models and other kinds of kinetic models.

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Received 28 August 2013
Revised 18 December 2013

DOI:https://doi.org/10.1103/PhysRevE.89.013307

Authors & Affiliations

Chuandong Lin¹, Aiguo Xu^2,3,*, Guangcai Zhang², Yingjun Li^1,†, and Sauro Succi⁴

¹State Key Laboratory for GeoMechanics and Deep Underground Engineering, China University of Mining and Technology, Beijing 100083, P.R. China
²National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009-26, Beijing 100088, P.R. China
³Center for Applied Physics and Technology, MOE Key Center for High Energy Density Physics Simulations, College of Engineering, Peking University, Beijing 100871, P.R. China
⁴Istituto Applicazioni Calcolo-CNR-Viale del Policlinico 137, 00161 Rome, Italy

^*Corresponding author: xu_aiguo@iapcm.ac.cn
^†Corresponding author: lyj@aphy.iphy.ac.cn

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Vol. 89, Iss. 1 — January 2014

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Physical Review E

covering statistical, nonlinear, biological, and soft matter physics