Toward Real-Time Simulation of Cardiovascular Flows by Introducing a Stabilized Frequency Finite Element Methods

The finite element methods for the solution of the Navier-Stokes equation have found common use for simulating cardiovascular flows. These simulations typically use periodic boundary conditions for physiological relevance. This results in a solution that is unsteady and often periodic. To capture this behavior, a conventional finite element method uses time-stepping to resolve the unsteady behavior of the flow to obtain cycle-to-cycle convergence. As a result, the overall cost of these simulations is significant. In fact, for most cardiovascular CFD simulations, more than 90% of the computational cost is spent on numerical convergence due to its unsteady and periodic nature. 

In this talk we propose an alternative way of simulating these flows in the frequency rather than the time domain, thereby obviating the need to simulate many cycles for convergence. In addition, since the periodic flows can be represented with a few modes in the frequency domain, we no longer need to rely on thousands of time steps to resolve the unsteady nature of these flows. We show that our formulation reduces the overall cost of a cardiovascular simulation by several orders of magnitude from hours or days to seconds or minutes. In this talk, we describe the underlying numerical method and compare it against the conventional time formulation when simulating hemodynamics in Norwood operation at low Reynolds number.