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Aymen Laadhari

Publications and source records attributed to Aymen Laadhari.

3 recordsLinked to original sources
arXiv2023

Numerical Approach Based on the Composition of One-Step Time-Integration Schemes For Highly Deformable Interfaces

In this work, we propose a numerical approach for simulations of large deformations of interfaces in a level set framework. To obtain a fast and viable numerical solution in both time and space, temporal discretization is based on the composition of one-step methods exhibiting higher orders and stability, especially in the case of stiff problems with strongly oscillatory solutions. Numerical results are provided in the case of ordinary and partial differential equations to show the main features and demonstrate the performance of the method. Convergence properties and efficiency in terms of computational cost are also investigated.

math.GM↗
arXiv2023

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

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.

math.GM↗