Daniel Castañón Quiroz

Assistant Professor

Orcid Profile

Education

• Ph.D. in Mathematics, Texas A&M, College Station, Texas, USA, 2016.
• B.S. in Applied Mathematics, IPN, Mexico City, Mexico, 2007.

Work Experience

Teaching currently

• Introduction to Spectral and Finite elements (in Spanish). Undergraduate Level Course. Semester 2025-II. Facultad de Ciencias--UNAM, Mexico City, Mexico.

Research Interests

• Numerical Analysis of Partial Differential Equations.
• Scientific Computing.
• Non-conforming, Hybrid and High-Order Finite Element Methods.
• Navier-Stokes. Porous Media.

Preprints

1.- DCQ, L. Jeannin, S. Lopez, and R. Masson. "Multi-segmented non-isothermal compositional liquid gas well model for geothermal processes". Submitted, 2024. HAL Preprint, ArXiv Preprint

Publications

1.- DCQ, and D. A. Di Pietro. "A Reynolds-semi-robust and pressure robust Hybrid High-Order method for the time dependent incompressible Navier--Stokes equations on general meshes". Accepted for publication in Computer Methods in Applied Mechanics and Engineering. December 2024. ArXiv Preprint, HAL Preprint.

2.- A. Armandine Les Landes, L. Beaude, DCQ, L. Jeannin, S. Lopez, F. Smai, T. Guillon and R. Masson, Geothermal Modeling in Complex Geological Systems with ComPASS. Accepted in Computer & Geosciences, November, 2024. HAL Preprint

3.- A. Armandine Les Landes, DCQ, L. Jeannin, S. Lopez, and R. Masson. Two-phase geothermal model with fracture network and multi-branch wells . SMAI Journal of Computational Mathematics, Volume 9 (2023). HAL-Preprint arXiv-Preprint.

4.- DCQ and D. A. Di Pietro, A pressure-robust HHO method for the solution of the incompressible Navier-Stokes equations on general meshes. IMA Journal of Numerical Analysis, April 2023. HAL-Preprint arXiv-Preprint.

5.- DCQ, D. A. Di Pietro, and A. Harnist, A Hybrid High-Order method for incompressible flows of non-Newtonian fluids with power-like convective behaviour. IMA Journal of Numerical Analysis, December, 2021. HAL-Preprint, arXiv-Preprint.

6.- M. Botti, DCQ, D. A. Di Pietro, and A. Harnist, A Hybrid High-Order method for creeping flows of non-Newtonian fluids. ESAIM: Math. Model Numer. Anal., Volume 55, Number 5, September-October 202, 2021. HAL-Preprint, arXiv-Preprint.

7.- DCQ and D. A. Di Pietro, A Hybrid High-Order method for the incompressible Navier--Stokes problem robust for large irrotational body forces , Comput. Math. Appl.,79-9, 2020. Preprint

8.- C. Nore, DCQ, L. Cappanera and J.-L. Guermond, Numerical Simulation of the Von-Karman-Sodium Experiment. J. Fluid Mech., 854 (2018). Preprint

9.- C.E. Janson, A. Shiri, J. Jansson, M. Moragues, DCQ, L. Saavedra, C. Degirmenci and M. Leoni, Nonlinear Computations of Heave Motions for a Generic Wave Energy Converter. Proceedings of NAV 2018: 19th International Conference on Ship and Maritime Research, 2018. Preprint

10.- C. Nore, DCQ, L. Cappanera and J.-L. Guermond, Direct numerical simulation of the axial dipolar dynamo in the Von Karman Sodium experiment.EPL (Europhysics Letters), Volume 114, Number 6, July 2016. Preprint

11.- C. Nore, DCQ, J.-L. Guermond, J. Léorat and F. Luddens Numerical Dynamo Action in Cylindrical Containers. The European Physical Journal Applied Physics (2015), 70:31101. Preprint

Upcoming talks

• CFC 2025. Minisymposium: Polytopal Methods for PDES in Fluid Mechanics. March 17-20, 2025. Santiago de Chile, Chile.

Some Presentations

• An introduction to Hybrid High Order (HHO) methods with applications to incompressible fluid flows . NEMESIS Kick off Meeting 2024 (link). Montpellier, France. June 19--21, 2024.

• Hybrid High-Order methods for Incompressible Flows of Non-Newtonian Fluids . WONAPDE 2024 (link). Minisymposium: Recent Advances in (Hybridizable) Discontinuous Galerkin Methods and Applications. Concepción, Chile. January 15--19, 2024.

• A Hybrid High-Order method for the incompressible Navier-Stokes problem robust for large irrotational body forces. Coloquio de Matemáticas y Mecánica del IIMAS (link), Mexico City, Mexico. March 9, 2022.

• A two-phase geothermal model with fracture network and multi-branch wells for geothermal simulation. MexSIAM Annual Meeting (link), Mexico City, Mexico. June 21-23, 2021. Online presentation.

• A Hybrid High-Order method for the incompressible Navier-Stokes problem robust for large irrotational body forces. Séminaire Approx, EDP et Modèles aléatoires, LMPA, Université de Littoral, France. April 22, 2021. Online presentation.

Teaching Experience (in the Past)

• Fourier Analysis I (in Spanish). Undergraduate Level Course. Semester 2025-I. Facultad de Ciencias--UNAM, Mexico City, Mexico.


• Numerical Analysis for Ordinary Differential Equations (in Spanish). Master Level Course. Semester 2024-II. IIMAS-UNAM, Mexico City, Mexico.


• Introduction to Finite Elements: Practice and Applications (in Spanish). Bachelor Level Course. Semester 2024-I. Facultad de Ciencias-UNAM, Mexico City, Mexico.


• Theory, Practice and Applications of Finite Elements (in Spanish). Postgraduate level course. Semester 2023-II. IIMAS-UNAM, Mexico City, Mexico.


• Numerical Ordinary Differential Equations (in Spanish). Bachelor level course. Semester 2023-I. Facultad de Ciencias-UNAM, Mexico City, Mexico.


• Differential Calculus and Dynamical Systems (in French). Python Labs. Undergraduate level. Fall 2021. University Côte d'Azur, Nice, France.


• Numerical Methods for PDEs. Master level. Recitation and Labs (Matlab). Fall 2013. Texas A&M, USA.


• Engineering Mathematics I. Undergraduate level. Recitation and Labs (Matlab). Fall 2011. Texas A&M, USA.