On the Numerical Evaluation of Wall Shear Stress Using the Finite Element Method.

Area of Science:

• Computational fluid dynamics
• Biomedical engineering
• Cardiovascular research

Background:

• Wall shear stress (WSS) is a critical hemodynamic parameter in cardiovascular studies.
• Accurate numerical computation of WSS using finite element methods (FEM) presents challenges.
• Existing methods for WSS evaluation can be sensitive to discretization choices and mesh quality.

Purpose of the Study:

• To compare WSS results from different finite element discretizations.
• To quantify differences between continuous and discontinuous stress calculations.
• To introduce and evaluate a modified variationally consistent boundary-flux method for WSS computation.

Main Methods:

• Comparison of P1/P1 stabilized and Taylor-Hood P2/P1 mixed finite elements for velocity and pressure.
• WSS computation using a novel boundary-flux method and projection onto P1, DG-1, and DG-0 spaces.
• Application to benchmark 2D Stokes and 3D Poiseuille flows, and patient-specific aneurysm models.

Main Results:

• Boundary-flux and P1 projection methods yield equivalent results for P1/P1 elements.
• P2/P1 elements show faster convergence with boundary-flux in Poiseuille flow but are sensitive to pressure errors in complex geometries.
• P2/P1 elements demonstrate superior robustness to mesh size in aneurysm WSS and low shear area (LSA) calculations.

Conclusions:

• The choice of finite element space significantly impacts WSS accuracy, especially in complex geometries like aneurysms.
• The proposed boundary-flux method offers advantages but requires careful consideration of element choice and mesh refinement.
• Careful selection of finite element spaces is crucial for reliable WSS computations in cardiovascular applications.