A Finite Element Approach For Modeling Biomembranes In Incompressible Power-Law Flow

Aymen Laadhari; Ahmad Deeb

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arXiv · 2305.17226

A Finite Element Approach For Modeling Biomembranes In Incompressible Power-Law Flow

Aymen Laadhari·Ahmad Deeb

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Abstract

We present a numerical method to model the dynamics of inextensible biomembranes in a quasi-Newtonian incompressible flow, which better describes hemorheology in the small vasculature. We consider a level set model for the fluid-membrane coupling, while the local inextensibility condition is relaxed by introducing a penalty term. The penalty method is straightforward to implement from any Navier-Stokes/level set solver and allows substantial computational savings over a mixed formulation. A standard Galerkin finite element framework is used with an arbitrarily high order polynomial approximation for better accuracy in computing the bending force. The PDE system is solved using a partitioned strongly coupled scheme based on Crank-Nicolson time integration. Numerical experiments are provided to validate and assess the main features of the method.

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BibTeX RIS

Aymen Laadhari, Ahmad Deeb. 2023-05-26. A Finite Element Approach For Modeling Biomembranes In Incompressible Power-Law Flow. https://arxiv.org/abs/2305.17226

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