Robust data assimilation using mixed-norm optimization

Experimental data are often contaminated with outliers which in turn influence the quality of recovery in data assimilation techniques. We develop and present a computational framework based on mixed-norm optimization to determine flow fields from experimental measurements via a data-assimilation technique. More specifically, we use a variational adjoint-based methodology to balance a recovery error with a sparsity constraint, resulting in a saddle-point problem. The method shows promise in situations where only sparse measurements are available. Applications from mean-flow recovery at lower Reynolds numbers, as well as Reynolds-stress recovery at higher Reynolds numbers, will be presented.