A gas kinetic scheme for the Baer–Nunziato two-phase flow model

Pan, Liang; Zhao, Guiping; Tian, Bo; Wang, Shuanghu

doi:10.1016/j.jcp.2012.04.049

Cited by 12 publications

(17 citation statements)

References 30 publications

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“…It could be observed that the numerical results could converge to one of the solutions of this problem with the improvement of meshes. What is equally important is that the numerical results of our scheme converge to the numerical results of the scheme in with the increase of N . It corresponds to the discussion that when the additional collision terms that describe the collision with the particles of other phases reduce to 0, this BGK model reduces into the generalized BGK proposed in .…”

Section: Numerical Experimentsmentioning

confidence: 60%

“…What is equally important is that the numerical results of our scheme converge to the numerical results of the scheme in with the increase of N . It corresponds to the discussion that when the additional collision terms that describe the collision with the particles of other phases reduce to 0, this BGK model reduces into the generalized BGK proposed in . And it could be concluded that the scheme proposed in is the particular case of the current scheme with τ ij → ∞ .…”

Section: Numerical Experimentsmentioning

confidence: 60%

“…In the hyperbolic part, the collision time τ at the interface is identical with the definition in where

p_{i}^{a}

, a = s , g and i = l , r represent the pressure of solid and gaseous phase at each side of the interface.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…In [17], the overshoot and undershoot was not observed in the solid phase, but there still existed obvious error in the contour of solid velocity. Similar with the discussions in [27], the numerical flux could be obtained from the distribution functions at the interface and the iterative process is avoided in our scheme. In this test, the stiffened gas EOS Equation (3) is used.…”

mentioning

confidence: 98%

“…High-order BGK schemes have also been proposed [25]. Recently, a unified BGK scheme [26] was developed for all Knudsen number flows, which is an extension of the gas-kinetic BGK scheme from the continuum flow to the rarefied regime with the discretization of particle velocity space.A gas-kinetic scheme for the Baer-Nunziato two-phase flow model was presented in [27]. On the basis of the BGK model in which the effect of external force was taken into account [28], a generalized BGK model for the Baer-Nunziato model was proposed in which the non-conservative terms ware considered as the external forces.…”

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confidence: 99%

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A gas‐kinetic scheme for the modified Baer–Nunziato model of compressible two‐phase flow

Pan

Zhao

Wang

2012

Numerical Methods in Fluids

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SUMMARY Numerical methods for the Baer–Nunziato model of compressible two‐phase flow have attracted much attention in recent years. In this paper, a two‐phase Bhatnagar–Gross–Krook (BGK) model is constructed in which the non‐conservative terms in the Baer–Nunziato model are considered as the external forces and the collisions both with particles of their phases and other phases are taken into consideration. On the basis of this BGK model, the so‐called modified Baer–Nunziato model is derived and a gas‐kinetic scheme for this modified model is presented. The distribution functions are constructed at the cell interface based on the integral solutions of the BGK equations for both phases. Then, numerical fluxes can be obtained by taking moments of the distribution functions, and non‐conservative terms are explicitly introduced into the construction of numerical fluxes. In this method, not only the iterative processes in the exact Riemann solvers are eliminated but also the collisions with the particles of other phases are taken into account. Copyright © 2012 John Wiley & Sons, Ltd.

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Section: Numerical Experimentsmentioning

confidence: 60%

Section: Numerical Experimentsmentioning

confidence: 60%

“…In the hyperbolic part, the collision time τ at the interface is identical with the definition in where

p_{i}^{a}

, a = s , g and i = l , r represent the pressure of solid and gaseous phase at each side of the interface.…”

Section: Numerical Experimentsmentioning

confidence: 99%

mentioning

confidence: 98%

mentioning

confidence: 99%

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A gas‐kinetic scheme for the modified Baer–Nunziato model of compressible two‐phase flow

Pan

Zhao

Wang

2012

Numerical Methods in Fluids

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High‐order gas kinetic flux solver for viscous compressible flow simulations

Jiang,

Wu,

Yang

et al. 2024

Numerical Methods in Fluids

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Although the gas kinetic schemes (GKS) have emerged as one of the powerful tools for simulating compressible flows, they exhibit several shortcomings. Since the local solution of continuous Boltzmann equation with the Maxwellian distribution function is used to calculate the numerical fluxes at the cell interface, the flux expression in GKS is usually more complicated. In this paper, a high‐order simplified gas kinetic flux solver (GKFS) is presented for simulating two‐dimensional compressible flows. Circular function‐based GKFS (C‐GKFS), which simplifies the Maxwellian distribution function into the circular function, combined with an improved weighted essentially non‐oscillatory (WENO‐Z) scheme is applied to capture more details of the flow fields with fewer grids. As a result, a simple high‐order accurate C‐GKFS is obtained, which improves the computing efficiency and reduce its complexity to facilitate the practical application of engineering. A series of benchmark‐test problems are simulated and good agreement can be obtained compared with the references, which demonstrate that the high‐order C‐GKFS can achieve the desired accuracy.

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Gas kinetic flux solver based finite volume weighted essentially non-oscillatory scheme for inviscid compressible flows

Jiang

Yang

et al. 2023

Appl. Math. Mech.-Engl. Ed.

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A gas kinetic scheme for the Baer–Nunziato two-phase flow model

Cited by 12 publications

References 30 publications

A gas‐kinetic scheme for the modified Baer–Nunziato model of compressible two‐phase flow

A gas‐kinetic scheme for the modified Baer–Nunziato model of compressible two‐phase flow

High‐order gas kinetic flux solver for viscous compressible flow simulations

Gas kinetic flux solver based finite volume weighted essentially non-oscillatory scheme for inviscid compressible flows

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