4D large scale variational data assimilation of a turbulent flow with a dynamics error model

Pranav Chandramouli*, Etienne Memin, Dominique Heitz

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

35 Citations (Scopus)
59 Downloads (Pure)


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.

Original languageEnglish
Article number109446
Number of pages29
JournalJournal of Computational Physics
Publication statusPublished - 1 Jul 2020

Bibliographical note

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


  • 4D variation assimilation
  • Adjoint-optimisation
  • Dynamics error model
  • Stochastic flow dynamics
  • Turbulent wake flow


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