Who am I ?

I'm Yolhan Mannes, a phd student of the university of Toulon under the supervision of Mehmet Ersoy and Omer Eker and welcome to my personal website.

Here, you will find infos on my work at the laboratory IMATH, my teaching and how to contact me if you have any questions.

Here is a little summary,

• Scientific Baccaloreat optain in 2016,
• Degree of mathematic in the university of Toulon from 2016 to 2019,
• Master of applied mathematics in the university of Toulon from 2019 to 2021,
• Phd since 2021 still going.

Wanna see more ? Click on my photo and see my CV !

Welcome to my work section, where I showcase my expertise in blood flow simulations and numerical analysis. My thesis focused on the derivation and analysis of new models for blood flow in arteries, with a specific focus on their applications to aneurysms and macrocirculation.

Through my research, I have gained a deep understanding of the Navier Stokes equations and how they can be applied to model complex blood flow scenarios. I specialize in asymptotic analysis and numerical simulation, using these tools to gain insights into how different pressure gradients, flow rates, and geometries can impact blood flow in arteries.

One of my main areas of interest is aneurysm modeling. By using my models and simulations, I am able to analyze the behavior of aneurysms under different conditions and assess the risk of rupture. This work has the potential to improve diagnosis and treatment of this potentially life-threatening condition.

Through my work, I am constantly pushing the boundaries of what is possible in blood flow modeling and analysis. I am passionate about this field and dedicated to bringing my skills and expertise to every project I work on.

I considered reduced models to simplify the system while retaining key characteristics of the flow dynamics. I derived both a 1D and a 2D model, applying asymptotic analysis and integration.

For the 1D model, integration was performed per section, while for the 2D model, it was done per radius. The 2D model allows for curvilinear mid-segment arteries and non-circular cross sections, which expands the applicability of the model beyond the limitations of the 1D case, where such geometrical flexibility is not present.

By comparing these models, I gained insights into the trade-offs between computational efficiency and accuracy in capturing complex arterial geometries.