A rapid interpolation method of finding vascular CFD solutions with spectral collocation methods

Abstract

We propose a rapid interpolation method of computational fluid dynamics (CFD) solution based on the collocation method for vascular flows through the polynomial interpolation and present a proof-of-concept computation of our preliminary results. A rapid CFD can play a crucial role for some applications such as the hemodynamics assessment for human vasculature in the emergent situation. The CFD approach for the real-time assessment at the clinical level is, however, not a practical tool due to the computational complexity and the long time integration needed for the individual CFDs. We propose an efficient, accurate, yet fast interpolation method of finding CFD solutions that can be utilized for the real-time hemodynamic analysis for clinicians. The main idea of the method is to use the vascular library where vascular solutions with different parameter values are pre-computed and stored. The desired unknown CFD solution is obtained via the interpolation using the similar solutions from the library. We use the spectral collocation method for the individual CFD solutions. The collocation method makes it easier to map the solution from the physical domain to the reference domain for the interpolation using the homeomorphic transformation. The interpolation is then directly constructed using the solution fields at the collocation points. Our preliminary results for vascular flows of 3D stenosis show that the proposed method is fast and accurate.