Research
Material Point Method (MPM)
Currently, I am working on large deformation problems in structural mechanics related to hydrological hazard events. This area is particularly interesting for several reasons. On the one hand, civil structures can experience significant deformations and even fractures due to strong impacts, especially during water hazard events such as floods or landslides. On the other hand, most moving masses are modeled as solid materials that undergo these large deformations.
To address these challenges, I am using an enriched finite element-based technique known as the Material Point Method (MPM).
Let me show you a very simple two-dimensional example of a MPM problem, where we can observe the two different discretizations used in this method: the Background Mesh (similar to the Finite Element Mesh) and the particle discretization (material points, in red). A granular flow is considered here, moving downward due to gravitational forces.
An good overview about this method is: Material Point Method after 25 years theory, implementation and applications [Link].
My research focuses on developing and implementing stabilization techniques that addresses the inherent instabilities of incompressible materials (water would be an incompressible material, for example). The objective is to accurately simulate both solid and fluid incompressible problems using the MPM, clearly involved in an hidrological hazard event.
Computational fluid dynamics
Numerical simulations of viscoelastic fluid flow with high elasticity
The overarching goal of my thesis was to develop mathematical models and numerical methods to simulate viscoelastic flows with high elasticity using the Finite Element Method. The equations modeling viscoelastic fluid flow present numerous nonlinearities. Additionally, when the elasticity of the fluid dominates over the convective forces, new instabilities must be addressed. Accurately reproducing these conditions is considered one of the biggest challenges in computational rheology, as classical methods fail to capture high levels of elasticity.
Other projects in fluid dynamics
Numerical analysis of the aerodynamic loads on a tunnel wall separation
In this project, we studied the influence of one telescope on another concerning optical parameters. To conduct the study, we solved the Navier-Stokes equations on real terrain, accounting for temperature and using the Smagorinsky model to capture turbulence. We then calculated the optical parameters influenced by the air temperature.
Numerical analysis of the optical quality over a telescope
We evaluated the aerodynamic loads at the ends of constructed sections caused by transient flows due to train motion along the Mont-Royal tunnel. We conducted a CFD simulation using moving domains, where the tunnel geometry remained fixed while the train moved inside it. We employed an arbitrary Lagrangian-Eulerian strategy, solving the Navier-Stokes equations to account for this motion.
Other projects in computational mechanics
The numerical simulation of electromagnetic processes with hysteresis
The goal was to study and numerically simulate electromagnetic processes with hysteresis, specifically applied to crankshafts. In this project, I simulated the magnetization process of the crankshafts and subsequently the demagnetization process. This method is commonly used in automotive factories to detect fractures in crankshafts using fluorescent metal shavings.