An improved gas-kinetic BGK finite-volume method for three-dimensional transonic flow

May, Georg; Srinivasan, Balaji Vasan; Jameson, Antony

doi:10.1016/j.jcp.2006.05.027

Cited by 79 publications

(57 citation statements)

References 19 publications

(39 reference statements)

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“…The limiter generates a jump in the vertical velocity field. A direct remedy for this is to use the high-resolution interpolation, or modify the initial dissipative terms in f 0 to make these terms continuous across the cell interface [10]. However, this error due to the limiter could be ignored for small and modest Z.…”

Section: Onset Of Two-dimensional Compressible Convectionmentioning

confidence: 99%

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A three-dimensional multidimensional gas-kinetic scheme for the Navier–Stokes equations under gravitational fields

Tian

Chan

et al. 2007

Journal of Computational Physics

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This paper extends the gas-kinetic scheme for one-dimensional inviscid shallow water equations (J. Comput. Phys. 178 (2002), pp. 533-562) to multidimensional gas dynamic equations under gravitational fields. Four important issues in the construction of a well-balanced scheme for gas dynamic equations are addressed. First, the inclusion of the gravitational source term into the flux function is necessary. Second, to achieve second-order accuracy of a well-balanced scheme, the Chapman-Enskog expansion of the Boltzmann equation with the inclusion of the external force term is used. Third, to avoid artificial heating in an isolated system under a gravitational field, the source term treatment inside each cell has to be evaluated consistently with the flux evaluation at the cell interface. Fourth, the multidimensional approach with the inclusion of tangential gradients in two-dimensional and three-dimensional cases becomes important in order to maintain the accuracy of the scheme. Many numerical examples are used to validate the above issues, which include the comparison between the solutions from the current scheme and the Strang splitting method. The methodology developed in this paper can also be applied to other systems, such as semi-conductor device simulations under electric fields.

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Section: Onset Of Two-dimensional Compressible Convectionmentioning

confidence: 99%

“…In the past several years, a gas-kinetic BGK Navier-Stokes (BGK-NS) scheme has been developed for compressible Navier-Stokes equations [15,9,10]. It achieves success in computing viscous flow solutions, such as the hypersonic viscous and heat conducting flows [14].…”

Section: Introductionmentioning

confidence: 99%

A three-dimensional multidimensional gas-kinetic scheme for the Navier–Stokes equations under gravitational fields

Tian

Chan

et al. 2007

Journal of Computational Physics

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“…Being relatively little known, they are often confused with particle methods such as DSMC or Molecular Dynamics or with Lattice Boltzmann methods. Numerous gas-kinetic schemes have been developed over the latest twenty years [10,21,22,43,47] with the aim to achieve a physically more consistent mathematical model of fluid mechanics. Gas-kinetic schemes are more accurate than conventional schemes, and might be able to resolve shock-layers.…”

Section: Introductionmentioning

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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“…This study focuses on the GKS developed by Xu ( [19]) which has also been investigated by other researchers ( [12,16]) and has provided very good results in a number of cases, ranging from viscous-dominated, subsonic flows to hypersonics. It provides fluxes accurate to τ 2 and, consequently, a second-order turbulent stress tensor.…”

Section: Introductionmentioning

confidence: 99%

“…2 Gas-kinetic scheme A few gas-kinetic schemes for the solution of the Euler and the Navier-Stokes equations have been proposed in the 1990s ( [5,11,12,19,21] and references therein) as an alternative to the most popular schemes, which normally assume continuity of the flow or solve a Riemann problem at cells interfaces.…”

Section: Introductionmentioning

confidence: 99%

A gas-kinetic scheme for the simulation of turbulent flows

Righi¹

2012

AIP Conference Proceedings

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Numerical schemes derived from gas-kinetic theory can be applied to simulations in the hydrodynamics limit, in laminar and also turbulent regimes. In the latter case, the underlying Boltzmann equation describes a distribution of eddies, in line with the concept of eddy viscosity developed by Lord Kelvin and Osborne Reynolds at the end of the nineteenth century. These schemes are physically more consistent than schemes derived from the Navier-Stokes equations, which invariably assume infinite collisions between gas particles (or interactions between eddies) in the calculation of advective fluxes. In fact, in continuum regime too, the local Knudsen number can exceed the value 0.001 in shock layers, where gas-kinetic schemes outperform Navier-Stokes schemes, as is well known.Simulation of turbulent flows benefit from the application of gas-kinetic schemes, as the turbulent Knudsen number (the ratio between the eddies' mean free path and the mean flow scale) can locally reach values well in excess of 0.001, not only in shock layers. A further advantage of gaskinetic schemes is that the fluxes are accurate to τ 2 , for instance in the scheme developed in [19] for the finite-volume discretization. In laminar flow, this provides a better resolution of shocks and vortexes, whereas in turbulent flows, high-order fluxes allow for a better resolution of secondary flows in a manner comparable to higher-order turbulence models for the Navier-Stokes schemes.This study has investigated a few cases of shock -boundary layer interaction comparing a gas-kinetic scheme and a Navier-Stokes one, both with a standard k − ω turbulence model. Whereas the results obtained from the Navier-Stokes scheme are affected by the limitations of eddy viscosity two-equation models, the gas-kinetic scheme has performed much better without making any further assumption on the turbulent structures.

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An improved gas-kinetic BGK finite-volume method for three-dimensional transonic flow

Cited by 79 publications

References 19 publications

A three-dimensional multidimensional gas-kinetic scheme for the Navier–Stokes equations under gravitational fields

A three-dimensional multidimensional gas-kinetic scheme for the Navier–Stokes equations under gravitational fields

A Gas-Kinetic Scheme for Turbulent Flow

A gas-kinetic scheme for the simulation of turbulent flows

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