Padé-Legendre Interpolants for Gibbs Reconstruction

Hesthaven, Jan S.; Kaber, Sidi Mahmoud; Lurati, Laura

doi:10.1007/s10915-006-9085-9

Cited by 30 publications

(28 citation statements)

References 16 publications

(36 reference statements)

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“…Examples of this include Padè-Jacobi, Padè-Chebischev and Padè-Legendre approximants. Padè-Legendre (PL) approximants are used in the present work as described by Hesthaven et al (2006) and Chantrasmi et al (2009).…”

Section: Statistical Approachmentioning

confidence: 99%

Stochastic Variation of the Aero-Thermal Flow Field in a Cooled High-Pressure Transonic Vane Configuration

Salvadori

Carnevale

Ahlfeld

et al. 2017

European Conference on Turbomachinery Fluid Dynamics and Hermodynamics

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In transonic high-pressure turbine stages, oblique shocks originated from vane trailing edges impact the rear suction side of each adjacent vane. High-pressure vanes are usually cooled to tolerate the combustor exit temperature levels, which would reduce dramatically the residual life of a solid vane. Then, it is highly probable that shock impingement will occur in proximity of one of the coolant rows. It has already been observed that the presence of an adverse pressure gradient generates non-negligible effects on heat load due to the increase in boundary layer thickness and turbulence level, with a detrimental impact on the local adiabatic effectiveness values. Furthermore, the generation of a tornado-like vortex has been recently observed that could further decrease the efficacy of the cooling system by moving cold flow far from the vane wall. It must be also underlined that manufacturing deviations and in-service degradation are responsible for the stochastic variation of geometrical parameters. This latter phenomenon greatly alters the unsteady location of the shock impingement and the time-dependent thermal load on the vane. Present work starts from what is shown in literature and provides a highly-detailed description of the aero-thermal field that occurs on a model that represents the flow conditions occurring on the rear suction side of a cooled vane. The numerical model is initially validated against the experimental data obtained by the University of Karlsruhe during TATEF2 EU project, and then an uncertainty quantification methodology based on the probabilistic collocation method and on Padè's polynomials is used to consider the probability distribution of the geometrical parameters. The choice of aleatory unknowns allows to consider the mutual effects between shock-waves, trailing edge thickness and hole diameter. Turbulence is modelled by using the Reynolds Stress Model already implemented in ANSYS ® Fluent ® . Special attention is paid to the description of the flow field in the shock/boundary layer interaction region, where the presence of a secondary effects will completely change the local adiabatic effectiveness values.

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Section: Statistical Approachmentioning

confidence: 99%

Stochastic Variation of the Aero-Thermal Flow Field in a Cooled High-Pressure Transonic Vane Configuration

Salvadori

Carnevale

Ahlfeld

et al. 2017

European Conference on Turbomachinery Fluid Dynamics and Hermodynamics

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“…Many authors studied differential methods as coefficients of Taylor series, Legendre interpolation, Chebyshev interpolation, singular value decomposition [2][3][4][5] to obtain Padé approximants. …”

Section: Remarkmentioning

confidence: 99%

Padé approximants for finite time ruin probabilities

Xuan

2015

Journal of Computational and Applied Mathematics

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a b s t r a c tIn this article, we investigate Padé approximants of hyper-exponential to base on the first moments and the matrix-exponential representation of Padé approximated function. An explicit formula is given for the Laplace transform in the time to calculate finite time ruin probabilities of classical Cramer-Lundberg model. This formula generalizes the ultimate ruin probabilities formula of Asmussen and Rolski (1991) [12]. To illustrate this formula, several numerical examples with different values u are given.

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“…These approximations have been improved using techniques such as filtering [21] and Padé interpolants [19]. -Splines Foster and Richards [11] showed the existence of a Gibbs-like phenomenon with maximum overshoot of 13.4% of the size of the jump discontinuity for piecewise linear splines.…”

Section: The Approximation Of Discontinuous Functions Is a Difficult mentioning

confidence: 99%