Accelerating cardiovascular CFD simulations: solving the harmonics balance form of the Navier-Stokes equations

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, for most cardiovascular CFD simulations, more than 90% of the computational cost is spent on numerical convergence.

In this talk, we propose using an alternative form of the Navier-Stokes equation to simulate these flows in frequency modes rather than the time integration, 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 solver can achieve over 100 times speedup while preserving the full temporal-spatial information of a CFD simulation. We will present result for three patient-specific cases: a Glenn pulmonary flow, a cerebral flow, and a left coronary artery flow to demonstrate the effectiveness of our solver.