Abstract

The analysis of complex fluid mechanical phenomena is usually based on experimental or theroretical/numerical analysis. Both approaches provide valuable, but incomplete information. Experimental data is usually incomplete, in the sense that not every state variable is accessible by measurements in every point of the domain. On the other hand, numerical solutions often lack the proper initial and boundary conditions. Therfore computations do not match the real flow conditions, even if the modell is perfectly valid. To obtain a complete set of information of a real flow state, both approaches can be combined by means of data assimilation.

To this end we use a variational approach. That means the parameters, initial and boundary conditions of a numerical model are adapted until the numerical solution matches the experimental data with respect to a specific optimality condition. The required adaptation of a preliminary model (i.e. the gradient towards a better solution) is determined by aid of the adjoint equations. The assimilated numerical state contains the unknown/unmeasured quantities under the constraint of the applied model. Furthermore, the quality of experimental data is enhanced by the model acting as a filter, which can reduce measurement noise.

The application of an adjoint-based data assimilation for compressible flows will be presented with three different applications. The first application identifies sound sources. The second application deals with the determination of instantaneous pressure distributions based on PIV data. The third is the analysis of reactive flow configurations.

The numerical framework and its requirements on the computational infrastructure will be discussed in detail.