A high-order gas-kinetic Navier–Stokes flow solver

Li, Qibing; Xu, Kun; Fu, Song

doi:10.1016/j.jcp.2010.05.019

Cited by 104 publications

(99 citation statements)

References 29 publications

(44 reference statements)

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“…As a final remark, the BGK model is consistent with conservation laws with an unity Prandtl number; the heath flux must therefore be corrected for realistic fluids [43]. A number of publications ( [19,46,48] and references therein) demonstrate the good qualities of the scheme.…”

Section: A Gas-kinetic Scheme For Laminar Flowmentioning

confidence: 97%

“…Despite the fact that these higher-order expansions provide a more accurate model of unresolved fluctuations, no convincing applications to rarefied have been put forward so far (refer to the discussion in [6]). However, higher-order expansions are being used with gas-kinetic schemes [19,26] with the aim of achieving a higher accuracy and handling local rarefaction. This study relies on a first-order expansion.…”

Section: A Gas-kinetic Scheme For Laminar Flowmentioning

confidence: 99%

“…Gas-kinetic schemes are more accurate than conventional schemes, and might be able to resolve shock-layers. Besides, they are more suitable to high-order reconstruction [19,46,48] and may be used as a platform to investigate rarefied flow [20,45]. Since conservation laws such as the NavierStokes and Euler equations can be derived from the Boltzmann equation, as shown in [6,42], a gas-kinetic scheme is always consistent with a conventional one, within the validity boundaries of the latter.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: A Gas-kinetic Scheme For Laminar Flowmentioning

confidence: 97%

Section: A Gas-kinetic Scheme For Laminar Flowmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Gas-Kinetic Scheme for Turbulent Flow

Righi

2015

Flow Turbulence Combust

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“…(12) and Eq. (15) are omitted for simplicity and they can be determined by the spatial derivatives of macroscopic flow variables and the compatibility condition as follows [15] ⎧…”

Section: Gas-kinetic Flux Solvermentioning

confidence: 99%

A third-order compact gas-kinetic scheme on unstructured meshes for compressible Navier–Stokes solutions

Pan

2016

Journal of Computational Physics

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In this paper, for the first time a third-order compact gas-kinetic scheme is proposed on unstructured meshes for the compressible viscous flow computations. The possibility to design such a third-order compact scheme is due to the high-order gas evolution model, where a time-dependent gas distribution function at cell interface not only provides the fluxes across a cell interface, but also presents a time accurate solution for flow variables at cell interface. As a result, both cell averaged and cell interface flow variables can be used for the initial data reconstruction at the beginning of next time step. A weighted least-square procedure has been used for the initial reconstruction. Therefore, a compact third-order gas-kinetic scheme with the involvement of neighboring cells only can be developed on unstructured meshes. In comparison with other conventional high-order schemes, the current method avoids the Gaussian point integration for numerical fluxes along a cell interface and the multi-stage Runge-Kutta method for temporal accuracy. The third-order compact scheme is numerically stable under CFL condition CFL ≈ 0.5. Due to its multidimensional gas-kinetic formulation and the coupling of inviscid and viscous terms, even with unstructured meshes, the boundary layer solution and vortex structure can be accurately captured by the current scheme. At the same time, the compact scheme can capture strong shocks as well.

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“…With the discretization of particle velocity space, a unified gas-kinetic scheme (UGKS) has been developed for the flow study in entire Knudsen number regimes from rarefied to continuum ones [44,29,43]. Recently, with the incorporation of high-order initial reconstruction, high-order gas-kinetic schemes have been constructed [24,28,30]. The flux evaluation in the scheme is based on the moments of a time and space dependent gas distribution function evolved from an initially piece-wise discontinuous polynomials of macroscopic flow variables around a cell interface, where high-order spatial and temporal derivatives of flow variables are coupled nonlinearly.…”

Section: Introductionmentioning

confidence: 99%

A high-order gas-kinetic Navier–Stokes flow solver

Cited by 104 publications

References 29 publications

A Gas-Kinetic Scheme for Turbulent Flow

A Gas-Kinetic Scheme for Turbulent Flow

A third-order compact gas-kinetic scheme on unstructured meshes for compressible Navier–Stokes solutions

A third-order gas-kinetic scheme for three-dimensional inviscid and viscous flow computations

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