Efficient tensor-based sensor placement for turbulent flow reconstructions

This talk will address the question of determining sensor locations to optimally place a limited number of sensors, from which the collected data can be used to accurately recover the turbulent flow fields. Previous work has used a basis obtained using proper orthogonal decomposition to approximate the flow field and used row subset selection to obtain near-optimal interpolation points that determine sensor locations. However, this approach does not exploit the inherent multidimensional structure of the flow fields. To address this, we use a tensor-based approach to approximate the flow field and obtain near-optimal interpolation points along each tensor mode. The resulting approach has much lower storage requirements and is often more accurate for a comparable number of sensors. Numerical experiments on a variety of fluid problems, such as the Kolmogorov flow and seasurface temperature, will illustrate the performance of the proposed methods.