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.

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, Heat and Mass Transfer, and Multiphase Flow.

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

Recent News


08/2012 - Hector is awarded an ERC Starting Grant to undertake the project MuSIC- Modeling and SImulation of Cancer growth; Budget: 1405420 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

05/2012 - Fermin Navarrina and Hector Gomez will organize a Minisymposium on Isogeometric Analysis at Congreso de Metodos Numericos en Ingenieria, 25-28 June, 2013 in Bilbao. The deadline to submit an abstract is October, 15th, 2012.

04/2012 - Our paper on numerical simulation of the Swift-Hohenberg equation has been accepted for publication in Communications in Nonlinear Science and Numerical Simulation (link to paper).

02/2012 - Our paper on numerical simulation of the phase-field crystal equation has been accepted for publication in Computer Methods in Applied Mechanics and Engineering (link to paper)

12/2011 - Our paper "Isogeometric Analysis of the Cahn-Hilliard phase-field model" has become one of the most cited articles in Computer Methods in Applied Mechanics and Enginneering since 2007.

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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