Analysis and higher-order extension of the VC2 confinement scheme

Costes, M.; Juillet, F.

doi:10.1016/j.compfluid.2011.12.002

Cited by 8 publications

(20 citation statements)

References 16 publications

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“…The second way of research concerns the extension of the method to higher-order schemes. Such a development has already been successfully achieved for the linear transport equation (Costes and Juillet, 2010). Its extension to the Euler/RANS equations will allow taking advantage of both the anti-diffusive property of VC2 and the higher-accuracy of the scheme to better resolve the internal structure of the vortices and wakes.…”

Section: Bvi Test-casementioning

confidence: 95%

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Application of vorticity confinement to rotor wake simulations

Costes

Renaud

Rodriguez

et al. 2012

IJESMS

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The VC2 vorticity confinement technique introduced by Steinhoff for vortex dominated flows is presented. After a brief description of the formulation and of its theoretical developments, the method is applied to the simulation of helicopter rotor wakes, focusing on two configurations: the rotor in hover, for which the flow field is mainly driven by the wake characteristics, and the rotor in low-speed descent flight where BVI noise is created. The results obtained show the efficiency of the approach, which provides wake predictions of the same or even better quality as higher-order methods.

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Section: Bvi Test-casementioning

confidence: 95%

“…This property was more deeply investigated in Costes and Juillet, (2010), using the equivalent PDE of (16). The combination of the confinement and of the truncation error of (13) introduces a forcing term into the original PDE (12).…”

Section: Formulation and Analysismentioning

confidence: 96%

Application of vorticity confinement to rotor wake simulations

Costes

Renaud

Rodriguez

et al. 2012

IJESMS

View full text Add to dashboard Cite

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“…In the scalar case of the linear transport equation ∂u ∂t + c ∂u ∂x = 0 with c > 0 (1) the VC method will be simply referred to as 'confinement' since the transported variable does not specifically correspond to vorticity. Previous studies consisted in the investigation of confinement for high-order extensions of the Lax-Wendroff and Beam-Warming schemes [22,24]. In both of these cases an analysis of the space discretization is not straightforward as these schemes are coupled in space-time.…”

Section: One-dimensional Scalar Formulationmentioning

confidence: 99%

“…The second term of the right-hand side represents the leading dispersive error term, which comes from the discretization operator R m . Note however that the harmonic mean term is nonlinear and therefore its expansion yields mixed dispersive, dissipative and even singular error terms that cannot be straightforwardly analyzed [22]. This subject will be further addressed in section 3.…”

Section: One-dimensional Scalar Formulationmentioning

confidence: 99%

“…Even more so, since in the vast majority of cases VC can be applied independently of the choice of the underlying numerical scheme and is not restricted to a specific formulation. High-order extensions of VC were analyzed for the linear advection equation [22], showing that the asymptotic solution over long distances is the same for all orders of accuracy, albeit at a lower convergence rate for higher orders. The slower convergence rate is in accordance with the lower numerical error that is associated with higher-order schemes, indicating a sound basis for an extension to the Euler/Navier-Stokes equations.…”

Section: Introductionmentioning

confidence: 99%

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Development and analysis of high-order vorticity confinement schemes

2017

Self Cite

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High-order extensions of the Vorticity Confinement (VC) method are developed for the accurate computation of vortical flows, following the VC2 conservative formulation of Steinhoff. First, a high-order formulation of VC is presented for the case of the linear transport equation for decoupled schemes in space and time. A spectral analysis shows that the new nonlinear schemes have improved dispersive and dissipative properties compared to their linear counterparts at all orders of accuracy. For the Euler and Navier-Stokes equations, the original VC method is extended to 3 rd-and 5 th-order of accuracy, with the goal of developing a VC formulation that maintains the vorticity preserving capability of the original 1 st-order method and is suitable for application to high-order numerical simulations. The high-order extensions remain both independent of the choice of baseline numerical scheme and rotationally invariant since they are based on the Laplace operator. Numerical tests validate the increased order of accuracy, vorticity-preserving capability and compatibility of the VC extensions with high-order methods.

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Numerical investigations of the vortex feature-based vorticity confinement models for the assessment in three-dimensional vortex-dominated flows

Yuan

Vigevano

2022

Meccanica

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In order to improve the vortex resolution in aerodynamic wakes, a locally normalized vortex feature-based vorticity confinement method is implemented into the multi-block, structured computational fluid dynamics solver (ROSITA). In this method, the second vorticity confinement (VC2) scheme with two well-known vortex feature detection methods (non-dimensional Q criterion, non-dimensional $$\lambda _2$$ λ 2 criterion) is employed to counterbalance the truncation error introduced by the numerical discretization of the convective term. The flow field of two benchmark three-dimensional steady vortex-dominated cases, the NACA0015 wing and the Caradonna–Tung hovering rotor, is simulated with the implemented method. The improvements in aerodynamics prediction, vorticity preservation, computational stability, and efficiency are demonstrated. From the numerical results, the vortex feature-based confinement models significantly improve the computational stability, the aerodynamic loads prediction and vorticity preservation capability, especially for the $$\lambda _2$$ λ 2 –based VC2 model. In addition, it allows the use of higher confinement parameters on a coarse grid with a relatively higher computational efficiency to obtain better results than those of a finer grid.

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Analysis and higher-order extension of the VC2 confinement scheme

Cited by 8 publications

References 16 publications

Application of vorticity confinement to rotor wake simulations

Application of vorticity confinement to rotor wake simulations

Development and analysis of high-order vorticity confinement schemes

Numerical investigations of the vortex feature-based vorticity confinement models for the assessment in three-dimensional vortex-dominated flows

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