Anisotropic adaptive finite element method for modelling blood flow.

Area of Science:

• Computational fluid dynamics
• Biomedical engineering
• Numerical analysis

Background:

• Simulating blood flow in the cardiovascular system requires accurate and efficient computational methods.
• Traditional finite element methods (FEM) can be computationally expensive for complex geometries and transient flows.
• The pulsatile nature of blood flow presents unique challenges for numerical simulations.

Purpose of the Study:

• To present an adaptive anisotropic finite element method (FEM) for enhanced computational efficiency in cardiovascular blood flow simulations.
• To demonstrate the effectiveness of this method in reducing computational time while maintaining accuracy.
• To apply the method to realistic cardiovascular scenarios.

Main Methods:

• Utilized the SUPG formulation for transient 3D incompressible Navier-Stokes equations.
• Discretized pressure and velocity fields using linear finite elements.
• Implemented adaptivity based on average flow over a cardiac cycle.
• Derived error indicators to define an anisotropic mesh metric field.
• Employed mesh modification algorithms for anisotropic mesh adaptation.

Main Results:

• The adaptive anisotropic FEM achieved an order of magnitude reduction in computing time.
• No loss of accuracy was observed compared to uniform mesh analyses.
• Successfully applied to pulsatile flow in a straight vessel and a porcine aorta model with stenosis and bypass graft.

Conclusions:

• Adaptive anisotropic FEM is a highly efficient method for simulating blood flow.
• This approach offers significant computational advantages for cardiovascular research.
• The method shows promise for clinical applications requiring rapid and accurate hemodynamic analysis.