Computational Hemodynamics in 3D Vascular Geometries
Abstract
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.
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.
