Fourier Spectral Dynamic Data Assimilation: Interlacing CFD with 4D Flow MRI

Abstract

Most data assimilation studies, incorporating observations into computational blood flow simulations, have approached the problem exploiting the traditional mathematical formulation in the time domain, an approach that incurs huge computational cost. In this work, a new method is introduced to perform variational adjoint-based dynamic data assimilation. The work aims to combine the superiority of computational fluid dynamics with the advantages of phase-contrast magnetic resonance imaging and simultaneously taking into account the dynamic nature of the heart beat. In contrast to the traditional time-stepping schemes, the novel approach relies on the harmonically balanced momentum equations expressed in the frequency domain, while the combination of the corresponding solutions yields the periodic solution of the original problem. This work enables accurate characterization of the dynamic flow field in quite feasible and practicable wall clock times, which are otherwise difficult to be achieved using currently available dynamic data assimilation strategies.