Hector Gomez

Associate
Professor of Applied Mathematics

University of A Coruna, Spain

Tel: +34 981 167 000 Ext: 1415

e-mail: hgomez at udc dot es

University of A Coruna, Spain

Tel: +34 981 167 000 Ext: 1415

e-mail: hgomez at udc dot es

## Hector Gomez

## Crystal growth in a supercooled liquid

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

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 adress 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 may be found in

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

## Recent News

10/2011 - Hector Gomez will visit the
Institute for Computational Engineering and Sciences at the University
of Texas at Austin in November.

09/2011 - Hector Gomez, Kris van deer Zee, Thomas J.R. Hughes and John T. Oden are organizing a minisymposium on "Phase-field modeling in fluid mechanics, solid mechanics and life-sciences" at the World Congress on Computational Mechanics, Sao Paulo, Brazil, 2012. The deadline to submit an abstract is November 30th, 2011.

08/2011 - Published in Archives of Computational Methods in Engineering a paper on numerical simulation of aeroacoustics and turbulence.

07/2011 - Prof. Yuri Bazilevs visits our research group and gives a seminar entitled "Modeling and simulation of wind turbines using Isogeometric Analysis".

06/2011 - Published in Journal of Computational Physics a paper on new unconditionally stable methods for phase-fields models.

09/2011 - Hector Gomez, Kris van deer Zee, Thomas J.R. Hughes and John T. Oden are organizing a minisymposium on "Phase-field modeling in fluid mechanics, solid mechanics and life-sciences" at the World Congress on Computational Mechanics, Sao Paulo, Brazil, 2012. The deadline to submit an abstract is November 30th, 2011.

08/2011 - Published in Archives of Computational Methods in Engineering a paper on numerical simulation of aeroacoustics and turbulence.

07/2011 - Prof. Yuri Bazilevs visits our research group and gives a seminar entitled "Modeling and simulation of wind turbines using Isogeometric Analysis".

06/2011 - Published in Journal of Computational Physics a paper on new unconditionally stable methods for phase-fields models.

## Crack propagation in a ductile material

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

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.