Hybrid Finite-Volume-Particle Method for Dusty Gas Flows

Chertock, Alina; Cui, Shumo; Kurganov, Alexander

doi:10.5802/smai-jcm.23

Cited by 7 publications

(6 citation statements)

References 53 publications

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“…Here, we consider the shock tube problem -a classical test for methods designed for the numerical integration of the dynamical equations of a continuous medium, often referred to as the test of Sod [43]. This problem has been widely used to test computational schemes for a two-phase medium (see, e.g., [9,26,41]). The one-dimensional equations for the conservation of mass, momentum, and energy in a gas-dust medium in the notation of Sections 3 and 4.1 have the form…”

Section: Formulation Of the Dustyshock Problemmentioning

confidence: 99%

Analysis of Numerical Algorithms for Computing Rapid Momentum Transfers between the Gas and Dust in Simulations of Circumstellar Disks

2018

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Approaches used in modern numerical simulations of the dynamics of dust and gas in circumstellar disks are tested. The gas and dust are treated like interpenetrating continuous media that can exchange momentum. A stiff coupling between the gas and dust phases is typical for such disks, with the dust stopping time much less than the characteristic dynamical time scale. This imposes high demands on the methods used to simulate the dust dynamics. A grid, piecewise-parabolic method is used as the basic algorithm for solving the gas-dynamical equations. Numerical solutions obtained using various methods to compute the momentum exchanges are presented for the case of monodisperse dust. Numerical solutions are obtained for shock tube problem and the propagation of sound waves in a gas-dust medium. The studied methods are compared in terms of their ability to model media with (a) an arbitrary (short or long) dust stopping time, and (b) an arbitrary dust concentration in the gas (varying the dust to gas mass ratio from 0.01 to 1). A method for computing the momentum exchange with infinite-order accuracy in time is identified, which makes it possible to satisfy the conditions (a) and (b) with minimal computational costs. A first-order method that shows similar results in the test computations is also presented. It is shown that the proposed first-order method for monodisperse dust can be extended to a regime when the dust is polydisperse; i.e., a regime represented by several fractions with different stopping times. Formulas for computing the gas and dust velocities for polydisperse dust with each fraction exchanging momentum with the gas are presented. snyt@catalysis.ru 4 The commonly used term for this ratio, the "stopping time", can lead to confusion, since, in the approximation considered here, a particle does not acquire the velocity of the gas, but instead a constant velocity relative to the gas velocity.

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Section: Formulation Of the Dustyshock Problemmentioning

confidence: 99%

Analysis of Numerical Algorithms for Computing Rapid Momentum Transfers between the Gas and Dust in Simulations of Circumstellar Disks

2018

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“…Therefore, the development of multiscale method which connects the modeling in different flow regimes smoothly is necessary. Many studies targeting on the multiscale methods have been conducted for the gas-particle system, such as unified gas kinetic scheme (UGKS) [62,30,57], discrete unified gas kinetic scheme (DUGKS) [55], unified gas kinetic particle method (UGKP) [68,58], method of moment (MOM) [12,15,46,41], direct simulation Monte Carlo (DSMC) [4], hybrid finite-volume-particle method [9], etc.…”

Section: Introductionmentioning

confidence: 99%

Unified gas-kinetic wave-particle methods VI: Disperse dilute gas-particle multiphase flow

Yang,

Liu,

et al. 2021

Preprint

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In this paper, a unified gas-kinetic wave-particle scheme (UGKWP) for the disperse dilute gas-particle multiphase flow is proposed. In this study, the gas phase is always in the hydrodynamic regime. However, the particle phase covers different flow regimes from particle trajectory crossing to the hydrodynamic wave interaction with the variation of local particle phase Knudsen number. The UGKWP is an appropriate method for the capturing of the multiscale transport mechanism in the particle phase through its coupled wave-particle formulation. In the regime with intensive particle collision, the evolution of solid particle will be followed by the analytic wave with quasi-equilibrium distribution; while in the rarefied regime the non-equilibrium particle phase will be captured through particle tracking and collision, which plays a decisive role in recovering particle trajectory crossing behavior. The gas phase in the multiphase system is assumed to be stay in the continuum flow regime, and its evolution is mainly controlled by the Navier-Stokes equations with the interaction with particle phase. The gas-kinetic scheme (GKS) is employed for the simulation of gas flow. In the highly collision regime for the particles, no particles will be sampled in UGKWP and the wave formulation for solid particle with the hydrodynamic gas phase will reduce the system to the two-fluid Eulerian model. On the other hand, in the collisionless regime for the solid particle, the free transport of solid particle will be followed in UGKWP, and coupled system will return to the Eulerian-Lagrangian formulation for the gas and particle. The scheme will be tested for in all flow regimes, which include the non-equilibrium particle trajectory crossing, the particle concentration under different Knudsen number, and the dispersion of particle flow with the variation of Stokes number. A experiment of shock-induced particle bed fluidization is simulated and the results are compared with experimental measurements. These numerical solutions validate suitability of the proposed scheme for the simulation of gas-particle multiphase flow.

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“…The interaction between gas phase and dust phase is due to the drag force and interspecies heat conduction. Since the pressureless Euler equations may develop δ-shocks at isolated points or along the surfaces of co-dimension one [8], to numerically solve the dusty-gas equations is challenging. Several robust and accurate numerical schemes have been developed for the dusty-gas model, including the finite volume schemes developed by T. Saito [31], T. Saito et al [34], M. Pelanti, and R. J. Leveque [29], and the finite-volume-particle hybrid scheme developed by A. Chertock et al [8].…”

Section: Introductionmentioning

confidence: 99%

“…Since the pressureless Euler equations may develop δ-shocks at isolated points or along the surfaces of co-dimension one [8], to numerically solve the dusty-gas equations is challenging. Several robust and accurate numerical schemes have been developed for the dusty-gas model, including the finite volume schemes developed by T. Saito [31], T. Saito et al [34], M. Pelanti, and R. J. Leveque [29], and the finite-volume-particle hybrid scheme developed by A. Chertock et al [8]. Besides the dusty-gas flow model, there has been continuous interest and efforts on the development of numerical schemes for different flow regimes of gas-particle system, such as the direct numerical simulation (DNS) [46,17], direct simulation Monte Carlo (DSMC) [3], multiphase particle in cell (MP-PIC) [28,38,1,26,27], method of moments (MOM) [11,25,14,15], and hydrodynamic two-fluid solvers [35].…”

Section: Introductionmentioning

confidence: 99%

A unified gas-kinetic scheme for continuum and rarefied flows VI: Dilute disperse gas-particle multiphase system

Liu

Wang

2019

Journal of Computational Physics

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In this paper, a unified gas kinetic scheme (UGKS) for multiphase dilute gas-particle system is proposed. The UGKS multiphase (UGKS-M) is a finite volume method, which captures flow physics in the regimes from collisionless multispecies transport to the two-fluid hydrodynamic Navier-Stokes (NS) solution with the variation of Knudsen number, and from granular flow regime to dusty gas dynamics with the variation of Stokes number. The reason for preserving the multiscale nature in UGKS-M is mainly coming from the direct modeling of the flow physics in the scales of discrete cell size and time step, where the ratio of the time step over the particle collision time determines flow behavior in different regimes. For the particle phase, the integral solution of the kinetic equation is used in the construction of numerical flux, which takes into account the particle transport, collision, and acceleration. The gas phase, which is assumed to be in the continuum flow regime, evolves numerically by the gas kinetic scheme (GKS), which is a subset of the UGKS for the Navier-Stokes solutions. The interaction between the gas and particle phase is calculated based on a velocity space mapping method, which solves accurately the kinetic acceleration process. The stability of UGKS-M is determined by the CFL condition only. With the inclusion of the material temperature evolution equation of solid particles, once the total energy loss in inelastic collision transfers into particle material thermal energy, the UGKS-M conserves the total mass, momentum, and energy for the whole multiphase system.In the numerical tests, the UGKS-M shows good multiscale property in capturing the particle trajectory crossing (PTC), particle wall reflecting phenomena, and vortex-induced segregation of inertial particles under different Stokes numbers. The scheme is also applied to simulate shock induced fluidization problem and the simulation results agree well with experimental 1 arXiv:1802.04961v2 [physics.comp-ph] 11 Sep 2018 measurement.

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Hybrid Finite-Volume-Particle Method for Dusty Gas Flows

Cited by 7 publications

References 53 publications

Analysis of Numerical Algorithms for Computing Rapid Momentum Transfers between the Gas and Dust in Simulations of Circumstellar Disks

Analysis of Numerical Algorithms for Computing Rapid Momentum Transfers between the Gas and Dust in Simulations of Circumstellar Disks

Unified gas-kinetic wave-particle methods VI: Disperse dilute gas-particle multiphase flow

A unified gas-kinetic scheme for continuum and rarefied flows VI: Dilute disperse gas-particle multiphase system

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