GALCIT Colloquium

Modeling blood flow in the circulatory system is a crucial piece for customizing surgical operations for individual patients. However, the industrial-scale deployment of this technology is partly hindered by the prohibitive cost of existing CFD solvers. This talk introduces a time-spectral solver to address this challenge. Since cardiorespiratory flows have periodic and smooth dynamics, they can be well-approximated in the discrete setting using only a handful of Fourier modes. That small number, when compared to thousands of time steps required in a conventional CFD solver, implies orders of magnitude reduction in simulation cost. Additionally, the new method enables time parallelization as the computations across Fourier modes can be distributed across multiple processors. A significant portion of this presentation will be devoted to discussing the finite element method for solving the Navier-Stokes equations in the frequency domain. Cumulatively, the improvements offered by the new formulation can reduce the cost of a typical cardiorespiratory simulation from hours to seconds.