An extended gas-kinetic scheme for shock structure calculations

Liu, Sha; Yang, Yuehan; Zhong, Chengwen

doi:10.1016/j.jcp.2019.04.016

Cited by 19 publications

(7 citation statements)

References 38 publications

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“…The partial differential equations for the stress tensor and heat flux vector are transformed into nonlinear coupled algebraic equations using the adiabatic approximation (Myong 1999). The corresponding relations for the shock wave flow problem are obtained as (Jiang et al 2019;Liu, Yang & Zhong 2019), (6.12) where q(κ) is a nonlinear dissipation factor. Note that the equations are implicit, coupled and can be solved by iterative methods like the Newton method for given values of conserved variables and their derivatives.…”

Section: Comparison With Conventional Burnett Equationsmentioning

confidence: 99%

Improved theory for shock waves using the OBurnett equations

Jadhav

Gavasane²,

Agrawal

2021

J. Fluid Mech.

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The main goal of the present study is to thoroughly test the recently derived OBurnett equations for the normal shock wave flow problem for a wide range of Mach number ( $3 \leq Ma \leq 9$ ). A dilute gas system composed of hard-sphere molecules is considered and the numerical results of the OBurnett equations are validated against in-house results from the direct simulation Monte Carlo method. The primary focus is to study the orbital structures in the phase space (velocity–temperature plane) and the variation of hydrodynamic fields across the shock. From the orbital structures, we observe that the heteroclinic trajectory exists for the OBurnett equations for all the Mach numbers considered, unlike the conventional Burnett equations. The thermodynamic consistency of the equations is also established by showing positive entropy generation across the shock. Further, the equations give smooth shock structures at all Mach numbers and significantly improve upon the results of the Navier–Stokes equations. With no tweaking of the equations in any way, the present work makes two important contributions by putting forward an improved theory of shock waves and establishing the validity of the OBurnett equations for solving complex flow problems.

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Section: Comparison With Conventional Burnett Equationsmentioning

confidence: 99%

Improved theory for shock waves using the OBurnett equations

Jadhav

Gavasane²,

Agrawal

2021

J. Fluid Mech.

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“…One can view it as an empirical parameter. The limiting factor q(κ) is constructed considering the form of nonlinear coupled constitutive relations (NCCR) [25,26], and is expressed as √ 2β…”

Section: Prediction Solvermentioning

confidence: 99%

“…where −k∇T and 2µS ij correspond to the heat flux and stress in NS equation, C p is the specific heat at constant pressure. β is a molecular model coefficient [26] involved in the variable soft sphere (VSS) model [27,28] and is calculated as…”

Section: Prediction Solvermentioning

confidence: 99%

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A conservative implicit scheme for steady state solutions of diatomic gas flow in all flow regimes

Yuan

Zhong

2020

Computer Physics Communications

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An implicit multiscale method with multiple macroscopic prediction for steady state solutions of gas flow in all flow regimes is presented. The method is based on the finite volume discrete velocity method (DVM) framework. At the cell interface a multiscale flux with a construction similar to discrete unified gas-kinetic scheme (DUGKS) is adopted. The idea of the macroscopic variable prediction is further developed and a multiple prediction structure is formed. A prediction scheme is constructed to give a predicted macroscopic variable based on the macroscopic residual, and the convergence is accelerated greatly in the continuum flow regime. Test cases show the present method is one order of magnitude faster than the previous implicit multiscale scheme in the continuum flow regime.

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“…The second proof is to compare the total macroscopic properties of the gas ρ, u 0 , T and validate the results against single species results. This test case is well-studied and there are suitable experimental, e.g 43 , and numerical results, e.g 30,31,44 . As described earlier, the power law for the…”

Section: A Single Species Recoverymentioning

confidence: 99%

Numerical evaluation of novel kinetic models for binary gas mixture flows

2020

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Most flows of practical interest consist of mixture of gases. Therefore the capability to model a gas mixture flow is important. Kinetic models for multicomponent gases have been considered since the original Bhatnagar-Gross-Krook (BGK) model was formulated. BGK-derived models pose a number of difficulties, e.g. avoiding negative density and temperature(s). A distinct challenge of the BGK approximation lies in recovering correct transport coefficients in the continuum limit. Two new kinetic models for gas mixtures: a Shakhov-based model and an Ellipsoidal-Statistical (ES)-based model, were recently introduced. Both models are capable of modelling a binary mixture of monoatomic gases and account for separate species-mean velocity such that the species diffusion and velocity drift are accurately represented. The main advantage is the recovery of three correct transport coefficients in the hydrodynamic limit and as a result having a correct Prandtl number for the mixture. The goal of this paper is to numerically validate the two new kinetic models for a range of high-speed flows and demonstrate their capabilities and limitations. The models are first validated against known results for normal shocks, showing good agreement for species density and temperature profiles. Moreover, the importance of the Prandtl number correction is demonstrated with the evaluation of the heat flux. A parametric study demonstrates the variation in flow properties for different mass ratios between species and for different Mach numbers. Finally, the models are evaluated for the flow around a circular cylinder. A detailed comparison with Monte Carlo results demonstrates promising results from both kinetic models.

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An extended gas-kinetic scheme for shock structure calculations

Cited by 19 publications

References 38 publications

Improved theory for shock waves using the OBurnett equations

Improved theory for shock waves using the OBurnett equations

A conservative implicit scheme for steady state solutions of diatomic gas flow in all flow regimes

Numerical evaluation of novel kinetic models for binary gas mixture flows

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