In this paper a combined arbitrary Lagrange-Euler fictitious domain (ALE-FD) method for fluid-structure interaction problems in cardiovascular biomechanics is derived in terms of a weighted residual finite-element formulation. For both fluid flow of blood and solid mechanics of vascular tissue, the performance of tetrahedral and hexahedral Crouzeix-Raviart elements are evaluated. Comparable convergence results are found, although for the test cases considered the hexahedral elements are more accurate. The possibilities that are offered by the ALE-FD method are illustrated by means of a simulation of valve dynamics in a simplified left ventricular flow model.
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van de Vosse, F., de Hart, J., van Oijen, C. et al. Finite-element-based computational methods for cardiovascular fluid-structure interaction. Journal of Engineering Mathematics 47, 335–368 (2003). https://doi.org/10.1023/B:ENGI.0000007985.17625.43
- arbitrary Lagrange-Euler
- blood flow
- fictitious domain
- fluid-structure interaction
- vascular-tissue mechanics