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Verification of the coupled‐momentum method with Womersley's Deformable Wall analytical solution

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Vasilina Filonova, Christopher J. Arthurs, Irene E. Vignon‐Clementel, C. Alberto Figueroa

Original languageEnglish
Article numbere3266
Number of pages23
JournalInternational Journal For Numerical Methods In Biomedical Engineering
Early online date21 Oct 2019
DOIs
Accepted/In press10 Sep 2019
E-pub ahead of print21 Oct 2019

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Abstract

In this paper, we perform a verification study of the Coupled‐Momentum Method (CMM), a 3D fluid‐structure interaction (FSI) model which uses a thin linear elastic membrane and linear kinematics to describe the mechanical behavior of the vessel wall. The verification of this model is done using Womersley's deformable wall analytical solution for pulsatile flow in a semi‐infinite cylindrical vessel. This solution is, under certain premises, the analytical solution of the CMM and can thus be used for model verification. For the numerical solution, we employ an impedance boundary condition to define a reflection‐free outflow boundary condition and thus mimic the physics of the analytical solution, which is defined on a semi‐infinite domain. We first provide a rigorous derivation of Womersley's deformable wall theory via scale analysis. We then illustrate different characteristics of the analytical solution such as space‐time wave periodicity and attenuation. Finally, we present the verification tests comparing the CMM with Womersley's theory.

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