Inflow and initial conditions for direct numerical simulation based on adjoint data assimilation

Abstract

A method for generating inflow conditions for direct numerical simulations (DNS) of spatially-developing flows is presented. The proposed method is based on variational data assimilation and adjoint-based optimization. The estimation is conducted through an iterative process involving a forward integration of a given dynamical model followed by a backward integration of an adjoint system defined by the adjoint of the discrete scheme associated to the dynamical system. The approach's robustness is evaluated on two synthetic velocity field sequences provided by numerical simulation of a mixing layer and a wake flow behind a cylinder. The performance of the technique is also illustrated in a real world application by using PIV measurements to acquire the database. This method allows to denoise experimental velocity fields and to reconstruct a continuous trajectory of motion fields from discrete and unstable measurements.

Data assimilation of mean velocity from 2D PIV measurements of flow over an idealized airfoil

“…A study conducted by Gronskis et al (2013) illustrates this point quite well. They employed adjoint data assimilation to generate initial and inflow conditions for a DNS of flow around a cylinder at a Reynolds number of Re = 172.…”

“…The reader is referred to Gronskis et al (2013) for an example of data assimilation where the inflow boundary condition for cylinder flow is a tunable parameter of the underlying model equations.…”

Dense velocity reconstruction from tomographic PTV with material derivatives

“…This gradient could be approximated using finite differences, requiring N evaluations of the cost function, where N is the number of optimization variables. Following recent literature (Gronskis et al 2013;Yang et al 2015;Yegavian et al 2015;Lemke and Sesterhenn 2016;among others), an alternative and more cost-efficient method to calculate the gradient is provided by the adjoint approach. This approach gives the exact gradient, but more importantly the computational cost of the adjoint approach is approximately equal to only one evaluation of the cost function.…”

“…It should be remarked that the adjoint procedure within VIC+ is relatively simple in comparison with the adjoint procedure in the aforementioned literature, because many calculation steps within VIC+ are linear operations and because the procedure does not involve time-integration. Only the state at a single time-instant needs to be kept in memory for evaluation of the adjoint equations and therefore the method does not suffer from the typically large memory requirements for adjoint-based optimization techniques, which led to the proposal of for example a storage/recomputation strategy by Gronskis et al (2013). Appendix B contains a pseudo-code of the VIC+ method and Fig.…”

“…In recent literature on methods with similar weighting parameters, optimal setting is either left out for future research (e.g., Papadakis and Mémin 2008) or manually chosen on a case-bycase basis (Gronskis et al 2013;Gregson et al 2014; among others). In an optimization framework similar to VIC+, the 'FlowFit' method for interpolation of scattered data to an Eulerian grid ) makes use of weighting parameters to penalize differences between the reconstruction and the velocity and material derivative measurements, and other differences such as nonzero curvature and divergence depending on the flow properties (e.g., incompressibility and measurement uncertainty).…”