Solveur de type Godunov pour simuler les écoulements turbulents compressibles

Forestier, Alain; Hérard, Jean-Marc; Louis, Xavier

doi:10.1016/s0764-4442(97)86969-8

Cited by 20 publications

(7 citation statements)

References 8 publications

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“…A similar work has been reported when investigating the convective part of the K-epsilon model focusing on compressible ows ( 12]), or when dealing with second-moment compressible closures ( 4]). The whole shows that these models arising from statistical approach of turbulence contain two distinct pressure elds.…”

Section: Resultssupporting

confidence: 52%

An Exact Riemann Solver for Multicomponent Turbulent Flow

Declercq

Forestier

Hérard

et al. 2000

International Journal of Computational Fluid Dynamics

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This contribution's topic is the resolution of the hyperbolic system which describes a multicomponent turbulent ow. The model is written for an isentropic gas. We compute the exact solution of the Riemann Problem (RP) associated to the hyperbolic system. It is composed of constant states separated by rarefaction waves, or shock waves and a contact discontinuity. The selection of the admissible part of the shock curve is obtained by an entropic criterion. Compressive shock means entropic shock for only one of the two mathematical entropies found. This entropy is the total energy of the system. With these existence and uniqueness properties, we compute the exact solution of (RP) by a Smoller's kind of parameterization.

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Section: Resultssupporting

confidence: 52%

An Exact Riemann Solver for Multicomponent Turbulent Flow

Declercq

Forestier

Hérard

et al. 2000

International Journal of Computational Fluid Dynamics

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“…With these ingredients it is possible to construct a full Godunov scheme as has been successfully done in the related case of a k-ε type closure [3]. In this note, we will alternatively present an approximate numerical Riemann solver.…”

Section: The Basic System Of Non-conservative Equationsmentioning

confidence: 99%

“…Our particular choice of the variable Z has been inspired by previous work on k-ε type closures (cf. [8,9,3]). It leads to the desirable feature that the jump conditions (a) reduce to the exact Rankine-Hugoniot relations in the limit of zero turbulence, and that (b) are equivalent to the Riemann invariants in the case of linearly degenerate fields (cf.…”

Section: Roe-type Scheme For Non-conservative Systemsmentioning

confidence: 99%

An Approximate Riemann Solver for Second-Moment Closures

Brun¹,

Hérard²,

Jeandel³

et al. 1999

Journal of Computational Physics

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The hyperbolic convective subset of a second-moment turbulence closure for the Favreaveraged compressible Navier-Stokes equations can be written as [1]where ρ stands for the mean density, U is the density weighted mean velocity vector, R the Reynolds stress tensor with components R i j = u i u j , E the mean specific total energy, and p the mean pressure which can be expressed via the ideal gas law (with γ being the ratio of specific heats), viz.,For simplicity we will restrict the following presentation to flows with statistically two space dimensions, i.e., a variable vector W = (ρ, ρU, ρV, ρ E, ρ R 11 , ρ R 22 , ρ R 33 , ρ R 12 ) t , such that we can write the system in matrix-vector notation W ,t + (F i (W)) ,i = H(W, ∇W), i = 1, 2,990

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“…-Consider turbulent effects in the phases, as they result in the appearance of a "turbulent sound speed" (Forestier et al (1997) [5], Saurel et al (2003) [6], Lhuillier et al (2013) [7]). In the frame of shallow water flows, these effects have been studied in Richard and Gavrilyuk (2012) [8] and Gavrilyuk et al (2016) [9].…”

Section: Introductionmentioning

confidence: 99%

Models and methods for two-layer shallow water flows

Chiapolino

Saurel

2018

Journal of Computational Physics

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Two-layer shallow water models present at least two fundamental difficulties that are addressed in the present contribution. The first one is related to the lack of hyperbolicity of most existing models. By considering weak compressibility of the phases, a strictly hyperbolic formulation with pressure relaxation is obtained. It is shown to tend to the conventional two-layer model in the stiff pressure relaxation limit. The second issue is related to the non-conservative terms in the momentum equations. Analyzing the Riemann problem structure, local constants appear precisely at locations where the non-conservative products need definition. Thanks to these local constants, a locally conservative formulation of the equations is obtained, simplifying the Riemann problem resolution through a HLL-type Riemann solver. The method is compared to literature data, showing accurate and oscillation free solutions. Additional numerical experiments show robustness and accuracy of the method.

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Solveur de type Godunov pour simuler les écoulements turbulents compressibles

Cited by 20 publications

References 8 publications

An Exact Riemann Solver for Multicomponent Turbulent Flow

An Exact Riemann Solver for Multicomponent Turbulent Flow

An Approximate Riemann Solver for Second-Moment Closures

Models and methods for two-layer shallow water flows

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