Reduced-order estimation of nonstationary flows with electrical impedance tomography

In this paper, we consider the simultaneous reconstruction of a nonstationary concentration distribution and the underlying nonstationary flow field. As the observation modality, we employ electrical impedance tomography. Earlier studies have shown that such an estimation scheme is in principle possible since the evolution of an inhomogeneous concentration carries information also on the velocity field. These results have, however, been restricted to either stationary velocity fields or simplified non-physical models. In the general case, the estimation of the velocity field up to the fine details of the flow with diffuse tomography is impossible. In this paper we show, however, that it is possible to estimate a reduced-order representation of a physical fluid dynamics model, here the Navier-Stokes model, simultaneously with the concentration. This is accomplished by considering a proper orthogonal decomposition representation for the velocity field, and careful modelling of the uncertainties of the models, in particular, the subspace of the velocity field that is not estimated. We assess the approach with two numerical examples in which a projection of a vortex flow is reconstructed.