Research output: Contribution to journal › Article › Scientific › peer-review

**4D large scale variational data assimilation of a turbulent flow with a dynamics error model.** / Chandramouli, Pranav; Memin, Etienne; Heitz, Dominique.

Research output: Contribution to journal › Article › Scientific › peer-review

Chandramouli, P, Memin, E & Heitz, D 2020, '4D large scale variational data assimilation of a turbulent flow with a dynamics error model', *Journal of Computational Physics*, vol. 412, 109446. https://doi.org/10.1016/j.jcp.2020.109446

Chandramouli, P., Memin, E., & Heitz, D. (2020). 4D large scale variational data assimilation of a turbulent flow with a dynamics error model. *Journal of Computational Physics*, *412*, [109446]. https://doi.org/10.1016/j.jcp.2020.109446

Chandramouli P, Memin E, Heitz D. 4D large scale variational data assimilation of a turbulent flow with a dynamics error model. Journal of Computational Physics. 2020 Jul 1;412. 109446. https://doi.org/10.1016/j.jcp.2020.109446

@article{bcb3c796f4ab4e7e80e45578fcbded0c,

title = "4D large scale variational data assimilation of a turbulent flow with a dynamics error model",

abstract = "We present a variational assimilation technique (4D-Var) to reconstruct time resolved incompressible turbulent flows from measurements on two orthogonal 2D planes. The proposed technique incorporates an error term associated to the flow dynamics. It is therefore a compromise between a strong constraint assimilation procedure (for which the dynamical model is assumed to be perfectly known) and a weak constraint variational assimilation which considers a model enriched by an additive Gaussian forcing. The first solution would require either an unaffordable direct numerical simulation (DNS) of the model at the finest scale or an inaccurate and numerically unstable large scale simulation without parametrisation of the unresolved scales. The second option, the weakly constrained assimilation, relies on a blind error model that needs to be estimated from the data. This latter option is also computationally impractical for turbulent flow models as it requires to augment the state variable by an error variable of the same dimension. The proposed 4D-Var algorithm is successfully applied on a 3D turbulent wake flow in the transitional regime without specifying the obstacle geometry. The algorithm is validated on a synthetic 3D data-set with full-scale information. The performance of the algorithm is further analysed on data emulating large-scale experimental PIV observations.",

keywords = "4D variation assimilation, Adjoint-optimisation, Dynamics error model, Stochastic flow dynamics, Turbulent wake flow",

author = "Pranav Chandramouli and Etienne Memin and Dominique Heitz",

note = "Pranav Chandramouli now working at the TU Delft. Paper made at INRIA",

year = "2020",

month = jul,

day = "1",

doi = "10.1016/j.jcp.2020.109446",

language = "English",

volume = "412",

journal = "Journal of Computational Physics",

issn = "0021-9991",

publisher = "Elsevier",

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AU - Chandramouli, Pranav

AU - Memin, Etienne

AU - Heitz, Dominique

N1 - Pranav Chandramouli now working at the TU Delft. Paper made at INRIA

PY - 2020/7/1

Y1 - 2020/7/1

N2 - We present a variational assimilation technique (4D-Var) to reconstruct time resolved incompressible turbulent flows from measurements on two orthogonal 2D planes. The proposed technique incorporates an error term associated to the flow dynamics. It is therefore a compromise between a strong constraint assimilation procedure (for which the dynamical model is assumed to be perfectly known) and a weak constraint variational assimilation which considers a model enriched by an additive Gaussian forcing. The first solution would require either an unaffordable direct numerical simulation (DNS) of the model at the finest scale or an inaccurate and numerically unstable large scale simulation without parametrisation of the unresolved scales. The second option, the weakly constrained assimilation, relies on a blind error model that needs to be estimated from the data. This latter option is also computationally impractical for turbulent flow models as it requires to augment the state variable by an error variable of the same dimension. The proposed 4D-Var algorithm is successfully applied on a 3D turbulent wake flow in the transitional regime without specifying the obstacle geometry. The algorithm is validated on a synthetic 3D data-set with full-scale information. The performance of the algorithm is further analysed on data emulating large-scale experimental PIV observations.

AB - We present a variational assimilation technique (4D-Var) to reconstruct time resolved incompressible turbulent flows from measurements on two orthogonal 2D planes. The proposed technique incorporates an error term associated to the flow dynamics. It is therefore a compromise between a strong constraint assimilation procedure (for which the dynamical model is assumed to be perfectly known) and a weak constraint variational assimilation which considers a model enriched by an additive Gaussian forcing. The first solution would require either an unaffordable direct numerical simulation (DNS) of the model at the finest scale or an inaccurate and numerically unstable large scale simulation without parametrisation of the unresolved scales. The second option, the weakly constrained assimilation, relies on a blind error model that needs to be estimated from the data. This latter option is also computationally impractical for turbulent flow models as it requires to augment the state variable by an error variable of the same dimension. The proposed 4D-Var algorithm is successfully applied on a 3D turbulent wake flow in the transitional regime without specifying the obstacle geometry. The algorithm is validated on a synthetic 3D data-set with full-scale information. The performance of the algorithm is further analysed on data emulating large-scale experimental PIV observations.

KW - 4D variation assimilation

KW - Adjoint-optimisation

KW - Dynamics error model

KW - Stochastic flow dynamics

KW - Turbulent wake flow

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