Inflow stabilization for hemodynamic simulations using Stokesian regions

Abstract

Blood flow simulations in three-dimensional space pose the challenge of isolating the vascular domain of interest, which introduces artificial interfaces, both upstream and downstream, where boundary conditions must be prescribed. Vessel curvature, tortuosity, and blood flow pulsatility contribute to the complexity of performing these simulations. A common practice in defining boundary conditions is to prescribe Neumann-like boundary conditions over these boundaries. A typical numerical problem in such a setting is associated with the unbounded nature of the kinetic energy that enters into the system, either through antegrade upstream flow or through downstream retrograde flow. Lack of energy control in the continuum problem may become a source of numerical instability, resulting in corrupted simulations. In this work, we propose a novel approach to avoid these instabilities by considering a bulk fluid with specific properties in a small portion of the domain in the vicinity of such boundaries. More precisely, the convective term from the governing equations is nullified in these domain extensions, resulting in Stokesian regions. In contrast to the classical approach based on the inclusion of straight long extensions to allow flow development, the proposed approach involves dealing with small regions whose length is smaller than the vessel diameter, to control the kinetic energy with near zero added computational cost. This stabilization strategy is investigated within the context of the Transversally Enriched Pipe Element Method, which makes the implementation straightforward. Academic examples and patient-specific vascular geometries are employed to illustrate the performance of the proposed stabilization strategy.