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.

State estimation in turbulent channel flow from limited observations

“…Finally, T should not appreciably exceed the Lyapunov time scale (τ + σ = 48 at Re τ = 180 according to Nikitin (2018)). If T τ σ , any infinitesimal perturbation in the initial condition will exponentially amplify and the accuracy of the state estimation deteriorates (Li et al 2020;Chandramouli, Mémin & Heitz 2020). We start with a benchmark case ( § 3.1, case B1), where the velocity field is observed every eighth point in each dimension, including space and time.…”

Error covariance tuning in variational data assimilation: application to an operating hydrological model

“…If prior errors are supposed to be uncorrelated, an identity matrix is used directly as the initial covariance matrix in many cases (e.g. [Chandramouli et al, 2020]). Otherwise, correlated prior errors are often represented by a correlation kernel of Matérn-type, e.g.…”

Linear and nonlinear sensor placement strategies for mean-flow reconstruction via data assimilation

“…In parallel with the continuation of more classical approaches to address the closure problem in the RANS equations (Durbin 2018), the latter problem is currently revisited through the consideration of alternative strategies which may be interlinked, as will be detailed in the following: uncertainty quantification (Xiao & Cinnella 2019), data assimilation (Lewis, Lakshmivarahan & Dhall 2006) and data-driven modelling (Duraisamy, Iaccarino & Xiao 2019). In particular, data assimilation aims to merge experimental and numerical approaches in order to overcome their inherent limitations, namely the difficulty in accessing the whole state of the flow in experiments (Heitz, Mémin & Schnörr 2010; Suzuki 2012; Gillissen, Bouffanais & Yue 2019) and the lack of knowledge of the inputs and models in numerical simulations (Hayase 2015; Meldi & Poux 2017; Chandramouli, Mémin & Heitz 2020; Da Silva & Colonius 2020; Li et al. 2020).…”