Computational Hemodynamics in 3D Vascular Geometries

Simulating blood flow in realistic human vessel shapes is essential for studying hemodynamics relevant to medical conditions such as aneurysms. Real blood exhibits non-Newtonian behavior (viscosity varies with shear rate), which makes accurate and stable computer simulations particularly challenging. We present a robust computational method that reliably simulates three-dimensional (3D) blood flow using the Carreau non-Newtonian model in geometries with strong curvature and local complexity. The approach is implemented in a hybridizable discontinuous Galerkin (HDG) framework and combines three targeted techniques to address the key numerical dynamics: a discrete gradient-reconstruction to treat the shear-rate-dependent viscous term, interface lifting operators to control nonlinear trace couplings across element faces, and a rotational pressure-correction time stepping to stabilize pressure velocity coupling. At the fully discrete level we establish stability and accuracy results; numerical tests confirm the scheme's unconditional discrete energy-dissipation and optimal convergence properties. Importantly, 3D simulations in a fusiform aneurysm geometry with pronounced curvature and locally complex vessel morphology demonstrate that the proposed computer algorithm robustly captures characteristic hemodynamic behavior observed in clinic 'specifically, a wall-hugging high-speed path across the aneurysmal sac and an extended recirculation region inside the sac' while maintaining high accuracy and stability on such complex vascular geometries.