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

Gomez Lab News

January 2017

Our paper on simulation of tumor angiogenesis accepted in the Journal of the Royal Society Interface. Read the paper here

December 2016

Our paper on simulation of prostate cancer accepted in PNAS. Read the paper here

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.

Unstable Infiltration in Porous Media

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.

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.