Time-spectral methods for cardiovascular simulations

Traditionally, cardiovascular flows are simulated by means of time integration. That requires the use of thousands of time steps to accurately resolve the flow in time and allow for cycle-to-cycle convergence. In this talk, I propose a much cheaper alternative that eliminates the need for time integration and simulation of many cardiac cycles for convergence. The idea is to simulate cardiac flows in frequency rather than time domain. The resulting time-spectral method significantly reduces the cost of cardiorespiratory simulations as it enables accurate discretization of the solution using a handful of frequencies. The number of required frequencies, owing to the predominantly periodic and smooth nature of cardiac flows, is typically less than 10. As a result, we are able to reduce the cost of these calculations by several orders of magnitude. Additionally, time-spectral formulations are parallelizable in the frequency domain, further reducing the time-to-solution. In this talk, I present a few cases that demonstrate the capability of the proposed time-spectral formulation, showing how it reduces solution turnover time from hours to minutes.