Simulating blood flow in the frequency domain

Flow dynamics in the respiratory system or the blood flow in the human body caused by the rhythmic beating of the heart are inherently time-periodic phenomena. In this talk, I discuss the possibility of simulating these flows in the time-spectral (frequency) domain. I argue that such a shift in formulation can present a significant advantage over conventional methods that are formulated in time. I demonstrate this point through a realistic blood flow modeling problem, where I show the flow is well-approximated using 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 the number of computed unknowns. The result is a method that reduces the cost of a typical cardiorespiratory simulation from days to hours. I briefly discuss how a finite element method can be constructed to solve the Navier-Stokes equations in the frequency domain. That includes introducing a method that remains stable in strongly convective flows while maintaining computational efficiency in solving a large coupled system of nonlinear equations.