Associate Professor of Applied Mathematics
University of A Coruna, Spain
Tel: +34 981 167 000 Ext: 1415
e-mail: hgomez (at) udc (dot) es

Hector Gomez

Hector Gomez

Crystal growth in a supercooled liquid


Phase field
            crystal

Crystals surrounded by undercooled liquid tend to grow leading to fascinating patterns, such as, for example dendrites. This picture shows the atomic structure of two crystallites growing in a supercooled liquid. The image has been obtain using large-scale numerical simulation of the Phase Field Crystal equation. We developed a new time integration scheme that preserves the fundamental features of the continuum theory.

Separation of two immiscible liquids


Cahn-Hilliard

Two premixed phobic liquids tend to separate when they are quenched, leading to complex patterns. The Cahn-Hilliard equation is a classical continuum theory describing this phenomenon. This picture shows a snapshot of a numerical simulation of the Cahn-Hilliard equation using Isogeometric Analysis, and an adaptive time-stepping technique that permitted computing, apparently for the first time, stationary states in three dimensions. The numerical simulation of phase separation may have relevance, for example, in the development of biodiesel.

Unstable infiltration in porous media

Unstable gravity-driven infiltration into a porous
              medium

Infiltration of water in dry porous media is subject to a powerful gravity-driven instability, leading to the phenomenon of gravity fingering. Water infiltrates the soil through preferential flow paths rather than as a compact wetting front.

Our Research Statement


We develop new modeling and computer-based simulation techniques to address a number of problems in engineering, physics and life sciences. Particular research interests include Computational Mechanics, Complex Fluids, Phase-field Methods, Biomechanics, Tumor-growth modeling, and Multiphase Flow.

Some illustrative examples of our research may be found in the pictures below. Relevant publications and citation data may be found at Google Scholar or ResearcherID

Recent News


02/2014 - Ignacio Romero and Aurora Hernández-Machado visit the group.

01/2014 - Guillermo Vilanova gets an award in the Poster Competition of the IGA2014 Conference !

12/2013 - Hector's paper in collaboration with Alessandro Reali and Giancarlo Sangalli accepted for publication in Journal of Computational Physics.

12/2013 - Rakesh Dhote's paper in collaboration with Hector, Roderick Melnik and Jean Zu accepted for publication in Computational Mechanics.

11/2013 - Borja Gonzalez's paper in collaboration with Ignacio Romero and Hector accpeted in Communications in Nonlinear Science and Numerical Simulation.

10/2013 - Guillermo Vilanova's paper on coupling discrete random walks and continuum theories for tumor angiogenesis accepted for publication in Computational Mechanics.

09/2013 - Peter Galenko visits the group.

08/2013 - Nikolai Kropotin's paper in collaboration with Hector, Peter Galenko, and Ken Elder accepted for publication in Physical Review E.

07/2013 - Tomás Alarcón visits the group. Carles Bona joins the group.

06/2013 - Tom Hughes visits the group and receives an Honorary Doctorate from University of A Coruña !!! Alessandro Reali visits the group.

06/2013 - Hector will be Keynote Speaker at the 12th U.S. National Congress on Computational Mechanics.

04/2013 - Hector appointed member of the Young Academy of Europe

04/2013 - Ju Liu's paper in collaboration with Hector, John A. Evans, Thomas J.R. Hughes, and Chad M. Landis accepted for publication in Journal of Computational Physics.

04/2013 - David Gonzalez-Rodriguez and Ean Hin Ooi visit the group.

04/2013 - Uwe Thiele's paper in collaboration with Andrew Archer, Edgar Knobloch and Hector accepted for publication in Physical Review E.

03/2013 - Guillermo Vilanova's paper on simulation of tumor angiogenesis accepted for publication in International Journal for Numerical Methods in Biomedical Engineering.

03/2013 - Vasileios Vavourakis and Rakesh Dhote visit the group.

02/2013 - Hector to receive the 2012 Juan C. Simo Award to the best young researcher in the field of Computational Mechanics.  The award is given every year by the Spanish Society of Numerical Methods in Engineering (SEMNI). (Press releases: ABC, La Voz de Galicia, El Correo Gallego, El Ideal Gallego, La Opinion, Diario de Ferrol, Faro de Vigo, Instituto de la Ingeniería de España, La Opinión (Interview), Universidade de A Coruña)

01/2012 - Our paper on numericcal simulation of gravity-driven infiltration has been accepted for publication in Journal of Computational Physics (link to paper)

12/2012 - Francisco Guillén, Professor of Diferential Equations and Numerical Analysis at University of Sevilla, visits the group.

08/2012 - Hector is awarded an ERC Starting Grant to undertake the project MuSIC- Modeling and SImulation of Cancer growth; Budget: 1,405.420 Eur. (Press releases: ABC, ABC Agencias, La Vanguardia, La Voz de Galicia, terra NOTICIAS, El Correo Gallego, La Opinion, El Ideal Gallego, Axencia Galega de Noticas)

07/2012 - Hector will be Invited Speaker at The First NEMB Venice Workshop on Cancer Nanotechnology


Crack propagation in a ductile material

Crack
            propgation

Material properties at the macroscale are to a large extent controlled by complex microstructures exhibiting topological defects, such as, for example, vacancies, grain boundaries and dislocations. These defects are the result of complicated non-equilibrium dynamics that takes place on atomic length scales. This picture shows the microstrucure evolution on atomic length scales of a ductile material that undergoes fracture. The simulation has been performed approximating the Phase Field Crystal equation using a new time-stepping algorithm that inherits at the discrete level the fundamental physical features of the theory.

Water/water-vapor two phase flow

Navier-Stokes-Korteweg

Water/water-vapor two-phase flows are of great importance and appear, for example, in cavitation and implosion. This piecture show a simulation of two water-vapor bubbles right after having merged. We have employed large-scale numerical simulations of the Navier-Stokes-Korteweg equations.


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