On the Numerical Evaluation of Wall Shear Stress Using the Finite Element Method
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10502720" target="_blank" >RIV/00216208:11320/25:10502720 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=.mLRisHtOY" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=.mLRisHtOY</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/cnm.70086" target="_blank" >10.1002/cnm.70086</a>
Alternative languages
Result language
angličtina
Original language name
On the Numerical Evaluation of Wall Shear Stress Using the Finite Element Method
Original language description
Wall shear stress (WSS) is a crucial hemodynamic quantity extensively studied in cardiovascular research, yet its numerical computation is not straightforward. This work compares WSS results obtained from two different finite element discretizations, quantifies the differences between continuous and discontinuous stresses, and introduces a modified variationally consistent method for WSS evaluation through the formulation of a boundary-flux problem. Two benchmark problems are considered: a 2D Stokes flow on a unit square and a 3D Poiseuille flow through a cylindrical pipe. These are followed by investigations of steady-state Navier-Stokes flow in two image-based, patient-specific aneurysms. The study focuses on P1/P1 stabilized and Taylor-Hood P2/P1 mixed finite elements for velocity and pressure. WSS is computed using either the proposed boundary-flux method or as a projection of tangential traction onto first order Lagrange (P1), discontinuous Galerkin first order (DG-1), or discontinuous Galerkin zero order (DG-0) space. For the P1/P1 stabilized element, the boundary-flux and P1 projection methods yielded equivalent results. With the P2/P1 element, the boundary-flux evaluation demonstrated faster convergence in the Poiseuille flow example but showed increased sensitivity to pressure field inaccuracies in image-based geometries compared to the projection method. Furthermore, a paradoxical degradation in WSS accuracy was observed when combining the P2/P1 element with fine boundary-layer meshes on a cylindrical geometry, an effect attributed to inherent geometric approximation errors. In aneurysm geometries, the P2/P1 element exhibited superior robustness to mesh size when evaluating average WSS and low shear area (LSA), outperforming the P1/P1 stabilized element. Projecting discontinuous finite element functions into continuous spaces can introduce artifacts, such as the Gibbs phenomenon. Consequently, it is crucial to carefully select the finite element space for boundary stress calculations, not only in applications involving WSS computations for aneurysms.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/NU22-08-00124" target="_blank" >NU22-08-00124: Blood flow modelling in intracranial vessels in relationship to endothelium changes and development of intracranial aneurysms</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Journal for Numerical Methods in Biomedical Engineering
ISSN
2040-7939
e-ISSN
2040-7947
Volume of the periodical
41
Issue of the periodical within the volume
9
Country of publishing house
GB - UNITED KINGDOM
Number of pages
19
Pages from-to
e70086
UT code for WoS article
001583201900007
EID of the result in the Scopus database
2-s2.0-105015580444