Research

My research focuses on well-balanced finite volume methods for two-dimensional hyperbolic systems of balance laws, in particular the shallow-water system:

\begin{aligned} \partial_t h + \nabla\cdot(h\mathbf{u}) &= 0,\\ \partial_t (h\mathbf{u}) + \nabla\cdot\left(h\,\mathbf{u}\otimes\mathbf{u}\right) + \nabla\!\left(\tfrac{g}{2}h^2\right) &= g\,h\,\nabla H . \end{aligned}

where $h$ is the water depth, $\mathbf{u}$ the depth-averaged velocity, $g$ the gravitational acceleration and $H$ the depth of the bottom measured from a fixed reference level, so that the free surface is $\eta = h - H$ . A well-balanced scheme preserves steady states such as the lake at rest:

\eta = h - H = \text{const}, \qquad \mathbf{u} = \mathbf{0}.

I am currently developing a semi-implicit scheme for this system in two dimensions.

Publications

First paper under review; it will appear here as soon as the preprint is available.

Theses

2024
Navier–Stokes equations. Theory and numerical implementationMaster thesis, MSc in Mathematics, University of Málaga. With Honours.[Thesis and code (Lid-Driven Cavity)]
2022
Z-transform and applications to signals and systemsBachelor thesis, BSc in Mathematics, University of Málaga.

Research projects

2022 – 2026
Geo-INQUIRE: Geosphere INfrastructures for QUestions into Integrated REsearchEuropean Commission – Horizon Europe (101058518). PI: J. Macías Sánchez (UMA).European geoscience data and service infrastructures; at UMA, simulation of tsunamis and submarine landslides.
2023 – 2025
Artificial intelligence applied to coastal environment science, beach-user safety and nautical sports to boost the Blue Economy in AndalusiaComplementary Plan for Marine Sciences – Recovery, Transformation and Resilience Plan (NextGenerationEU). PIs: F. I. Franco Duro, J. Macías Sánchez.AI models to forecast jellyfish, floating aggregates and algae; Oceanaria–Andalucía website and mobile app.
2022 – 2024
HEU-tools: Tools for risk assessment, early warning and efficient computing for tsunamis, lava flows and landslidesSpanish Ministry of Science and Innovation – Proof of Concept Projects 2022. PIs: M. J. Castro Díaz, C. Parés Madroñal.

Research group and PhD

Member of the research group EDANYA (FQM-216) — Differential Equations, Numerical Analysis and Applications, University of Málaga, since 2025.

PhD student in the PhD Programme in Mathematics since 2025. Advisors: María de la Luz Muñoz Ruiz and Cipriano Escalante Sánchez. Tutor: Tomás Morales de Luna.