Application of Gas-Kinetic Scheme with Kinetic Boundary Conditions in Hypersonic Flow

Li, Qibing; Fu, Song; Xu, Kun

doi:10.2514/1.14130

Cited by 53 publications

(35 citation statements)

References 16 publications

(30 reference statements)

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“…For a local equilibrium state with f = g, the Euler equations can be obtained by taking the moments of ψ α to Eq. (19). This yields…”

Section: The Gas-kinetic Schemementioning

confidence: 79%

“…In the past years, a gas-kinetic scheme (GKS) based on the BGK model [7] has been developed for the compressible flow simulation under linear polynomials for the mass, momentum, and energy distributions separated by discontinuities at the origin [27,21]. The GKS has been successfully applied in many engineering applications, especially for the hypersonic viscous and heat conducting flows [28,18,19].…”

Section: Introductionmentioning

confidence: 99%

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Comparison of the generalized Riemann solver and the gas-kinetic scheme for inviscid compressible flow simulations

2011

Journal of Computational Physics

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The generalized Riemann problem (GRP) scheme for the Euler equations and gaskinetic scheme (GKS) for the Boltzmann equation are two high resolution shock capturing schemes for fluid simulations. The difference is that one is based on the characteristics of the inviscid Euler equations and their wave interactions, and the other is based on the particle transport and collisions. The similarity between them is that both methods can use identical MUSCL-type initial reconstructions around a cell interface, and the spatial slopes on both sides of a cell interface involve in the gas evolution process and the construction of a time-dependent flux function. Although both methods have been applied successfully to the inviscid compressible flow computations, their performances have never been compared. Since both methods use the same initial reconstruction, any difference is solely coming from different underlying mechanism in their flux evaluation. Therefore, such a comparison is important to help us to understand the correspondence between physical modeling and numerical performances. Since GRP is so faithfully solving the inviscid Euler equations, the comparison can be also used to show the validity of solving the Euler equations itself. The numerical comparison shows that the GRP exhibits a better computational efficiency, and has comparable accuracy with GKS for the Euler solutions in 1D case, but the GKS is more robust than GRP. For the 2D high Mach number flow simulations, the GKS is absent from the shock instability and converges to the steady state solutions faster than the GRP. The GRP has carbuncle phenomena, likes a cloud hanging over exact Riemann solver. The GRP and GKS use different physical processes to describe the flow motion starting from a discontinuity. One is based on the assumption of equilibrium state with infinite number of particle collisions, and the other starts from the non-equilibrium free transport process to evolve into an equilibrium one through particle collisions. The different mechanism in the flux evaluation deviates their performance. Through this study, we may conclude scientifically that it is NOT valid to use the Euler equations to construct numerical fluxes in a discretized space. To adapt Navier-Stokes (NS) Preprint submitted to Elsevier 31 October 2010 equations is NOT valid either because the NS has no any account on the strength of the discontinuity. A direct modeling of the physical process in the discretized space is necessary in the construction of numerical scheme. This process is similar to the modeling in deriving the governing equations, but the control volume here cannot be shrunk to zero.

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“…For a local equilibrium state with f = g, the Euler equations can be obtained by taking the moments of ψ α to Eq. (19). This yields…”

Section: The Gas-kinetic Schemementioning

confidence: 79%

Section: Introductionmentioning

confidence: 99%

Comparison of the generalized Riemann solver and the gas-kinetic scheme for inviscid compressible flow simulations

2011

Journal of Computational Physics

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“…The idea of a kinetic wall boundary condition has been adapted from [10,18,44]. The fluxes are calculated by modelling the gas evolution stage within the gas-kinetic solver starting from a "wall" state and a "flow" state.…”

Section: Kinetic Wall Boundary Conditionmentioning

confidence: 99%

A Gas-Kinetic Scheme for Turbulent Flow

Righi

2015

Flow Turbulence Combust

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RANS simulations may not provide accurate results for all flow conditions. The interaction between a shock wave and a turbulent boundary layer is an example which may still be difficult to simulate accurately. Beside the inability to reproduce physical phenomena such as shock unsteadiness, the argument is put forward that the conventional numerical schemes, based on the Navier-Stokes equations, may be unable to generate a physically consistent turbulent stress tensor in the presence of large unresolved scales of motion. A large ratio between unresolved and resolved scales of motion, a sort of Knudsen number based on turbulent fluctuations, might introduce inaccuracies for which the turbulence model is not accountable. In order to improve the accuracy of RANS simulations, researchers have suggested various ad-hoc modifications to standard turbulence models which limit eddy viscosity or the turbulent stress tensor in the presence of strong gradients. Gas-kinetic schemes might be able to improve RANS predictions in shocklayers by removing or limiting the errors caused by the large scales ratio. These schemes are a class of their own; in the framework of a finite-volume or finite-elements discretizations, they model the numerical fluxes on the basis of the Boltzmann equation instead of the Navier-Stokes equations as is conventionally done. In practical terms, these schemes provide a higher accuracy and, more importantly, an in-built "multiscalar" mechanism, i.e. the ability to adjust to the size of unresolved scales of motion. This property makes them suitable for shock-capturing and rarefied flow. Gas-kinetic scheme may be coupled to a conventional RANS turbulence model; it is shown that the turbulent stress tensor is naturally adjusted as a function of the unresolved-toresolved scales ratios and achieves a higher physical consistency than conventional schemes. The simulations shown -well-known benchmark cases with strong shock-boundary layer interactions -have been obtained with a standard two-equation turbulence model (k-ω). It is shown that the gas-kinetic scheme provides good quality predictions, where conventional schemes with the same turbulence model are known to fail.

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“…Eqs. (23)- (26), can be also used for the NSE [33], the TTKM [2] and even the Burnett equations [32], where only the gas distribution function f in at the inner side of the wall needs to be constructed based on different models. For example, for the NSE calculation the distribution function f in in Eqs.…”

Section: Wall Boundary Conditionmentioning

confidence: 99%

“…(24)- (26) should be constructed using the NSE numerical solutions of the neighboring cells inside the computational domain [33], we may denote it by f in NSE here. Similarly, for the TTKM simulation [33], we need to construct f in TTKM in using Eqs. (24)- (26).…”

Section: Wall Boundary Conditionmentioning

confidence: 99%

Multiple temperature kinetic model and its applications to micro-scale gas flows

Liu

Zhu

et al. 2012

Computers & Fluids

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a b s t r a c tThis paper presents a gas-kinetic scheme to solve the multiple temperature kinetic model (MTKM), which was proposed in J. Comput. Math. 29(6) (2011) 639-660, for the study of non-equilibrium flows. The MTKM is a two-stage particle collision model possessing an intermediate quasi-equilibrium state with a symmetric second-order temperature tensor. A gas-kinetic finite volume scheme is developed for the numerical solution of the MTKM in the continuum and transition flow regimes. The gas-kinetic scheme is designed for the updating of macroscopic variables, which include the conservative flow variables and the multiple temperature field. In order to validate the kinetic model, the gas-kinetic scheme is used in the study of lid-driven cavity flows in both continuum and transition flow regimes. The numerical results predicted by the MTKM are compared with those from the direct simulation Monte Carlo (DSMC) method, the Navier-Stokes equations (NSE), and the early three-temperature kinetic model (TTKM) proposed in Phys. Fluids 19, 016101(2007). It is demonstrated that the MTKM has obvious advantages in comparison with the NSE and the TTKM in capturing the non-equilibrium flow behavior in the transition flow regime. One distinguishable phenomenon captured by the MTKM is that in the transition flow regime the heat flux direction can be from a low temperature to a high temperature region, which violates the Fourier's law of continuum flows. The MTKM provides a more accurate physical model than the NSE for the non-equilibrium flows.

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Application of Gas-Kinetic Scheme with Kinetic Boundary Conditions in Hypersonic Flow

Cited by 53 publications

References 16 publications

Comparison of the generalized Riemann solver and the gas-kinetic scheme for inviscid compressible flow simulations

Comparison of the generalized Riemann solver and the gas-kinetic scheme for inviscid compressible flow simulations

A Gas-Kinetic Scheme for Turbulent Flow

Multiple temperature kinetic model and its applications to micro-scale gas flows

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