New Trends in Ensemble Forecast Strategy: Uncertainty Quantification for Coarse-Grid Computational Fluid Dynamics

Resseguier, Valentin; Li, Long; Jouan, Gabriel; Dérian, Pierre; Mémin, Étienne; Chapron, Bertrand

doi:10.1007/s11831-020-09437-x

Cited by 33 publications

(54 citation statements)

References 147 publications

(194 reference statements)

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“…However, besides potential energy conservation issues, the noise covariance is often not explicit enough, and has to be simplified and estimated using the available data. Interested readers can refer to [64], and references herein, for more detailed reviews on model error specification in coarse-scale computational fluid dynamics (CFD). For ROM UQ, [73] propose distributions and efficient sampling methods for the projection matrices in Galerkin-projection-based dimensionality reduction methods.…”

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confidence: 99%

“…This operator -or equivalently the spatial covariance of the residual velocity -can be modeled or learned from data. The review [64] describes some of the many choices that have been explored in this vein. This includes for instance parametric models based on fluid velocity self-similarity or brute-force non-parametric covariance estimation from highresolution datasets.…”

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confidence: 99%

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Quantifying Truncation-Related Uncertainties in Unsteady Fluid Dynamics Reduced Order Models

Resseguier¹,

Picard²,

Mémin³

et al. 2021

SIAM/ASA J. Uncertainty Quantification

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In this paper, we present a new method to quantify the uncertainty introduced by the drastic dimensionality reduction commonly practiced in the field of computational fluid dynamics, the ultimate goal being to simulate accurate priors for real-time data assimilation. Our key ingredient is a stochastic Navier-Stokes closure mechanism that arises by assuming random unresolved flow components. This decomposition is carried out through Galerkin projection with a Proper Orthogonal Decomposition (POD-Galerkin) basis. The residual velocity fields, model structure and evolution of coefficients of the reduced order's solutions are used to compute the resulting multiplicative and additive noise's correlations. The low computational cost of these consistent correlation estimators makes them applicable to the study of complex fluid flows. This stochastic POD-ROM is applied to 2D and 3D DNS wake flows at Reynolds 100 and 300, respectively, with Uncertainty Quantification (UQ) and forecasting outside the learning interval being the main focus. The proposed stochastic POD-ROM approach is shown to stabilize the unstable temporal coefficients and to maintain their variability under control, while exhibiting an impressively accurate predictive capability.

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confidence: 99%

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confidence: 99%

Quantifying Truncation-Related Uncertainties in Unsteady Fluid Dynamics Reduced Order Models

Resseguier¹,

Picard²,

Mémin³

et al. 2021

SIAM/ASA J. Uncertainty Quantification

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“…As pointed out by Resseguier et al [16], it corresponds to a velocity induced by the unresolved eddies, that is linked to the turbophoresis phenomenon detectable in geophysical flows; i.e., the tendency of the fluid-particle to migrate in the direction of less energetic turbulence. Diffusion due to SUS: the last two terms on the right-hand side of Equation (19) account for the turbulent diffusion; the variance tensor plays the role of a diffusion tensor similar to a generalised eddy-viscosity coefficient. Both deformation rate and rotation-rate contribute to diffusion, unlike in the classical eddy-viscosity model.…”

Section: Physical Interpretationmentioning

confidence: 99%

“…The LU model was tested in several cases: in a series of papers Resseguier et al [16][17][18][19], as well as Bauer et al [20,21], successfully used this model to study geophysical flows. It was found to be more accurate in the reproduction of extreme events and to provide a new analysis tool.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Modelling of Turbulent Flows for Numerical Simulations

Cintolesi

Mémin

2020

Fluids

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Numerical simulations are a powerful tool to investigate turbulent flows, both for theoretical studies and practical applications. The reliability of a simulation is mainly dependent on the turbulence model adopted, and improving its accuracy is a crucial issue. In this study, we investigated the potential for an alternative formulation of the Navier–Stokes equations, based on the stochastic representation of the velocity field. The new approach, named pseudo-stochastic simulation (PSS), is a generalisation of the widespread classical eddy–viscosity model, where the contribution of the unresolved scales of motion is expressed by a variance tensor, modelled following different paradigms. The PSS models were compared with the classical ones mathematically and numerically in the turbulent channel flow at R e τ = 590 . The PSS and the classical models are equivalent when the variance tensor is shaped through a molecular dissipation analogy, while it is more accurate when the tensor is defined by the way of a local variance model. A near-wall damping function derived from recent advancement in the field is also proposed and was successfully validated. The analyses demonstrate the relevance of the approach proposed and provide a basis for the development of an alternative turbulence model.

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“…The performance of such a random model has been evaluated and analyzed in terms of uncertainty quantification and ensemble forecasting (Resseguier et al, 2019) for a surface quasi-geostrophic (SQG) flow. A more efficient spread is produced by the proposed model compared to a deterministic model with perturbed initial condition.…”

Section: Introductionmentioning

confidence: 99%

Stochastic representation of mesoscale eddy effects in coarse-resolution barotropic models

Bauer

Chandramouli

et al. 2020

Ocean Modelling

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A stochastic representation based on a physical transport principle is proposed to account for mesoscale eddy effects on the evolution of the large-scale flow. This framework arises from a decomposition of the Lagrangian velocity into a smooth in time component and a highly oscillating term. One important characteristic of this random model is that it conserves the energy of any transported scalar. Such an energy-preserving representation is tested for the coarse simulation of a barotropic circulation in a shallow ocean basin, driven by a symmetric double-gyres wind forcing. The empirical spatial correlation of the random small-scale velocity is estimated from data of an eddy-resolving simulation. After reaching a turbulent equilibrium state, a statistical analysis of tracers shows that the proposed random model enables us to reproduce accurately, on a coarse mesh, the local structures of the first four statistical moments (mean, variance, skewness and kurtosis) of the high-resolution eddy-resolved data.

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New Trends in Ensemble Forecast Strategy: Uncertainty Quantification for Coarse-Grid Computational Fluid Dynamics

Cited by 33 publications

References 147 publications

Quantifying Truncation-Related Uncertainties in Unsteady Fluid Dynamics Reduced Order Models

Quantifying Truncation-Related Uncertainties in Unsteady Fluid Dynamics Reduced Order Models

Stochastic Modelling of Turbulent Flows for Numerical Simulations

Stochastic representation of mesoscale eddy effects in coarse-resolution barotropic models

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