National Autonomous University of Mexico (UNAM)

Insitute of Mathematics, Campus Juriquilla

New Webpage Here

2011-214:

Postdoctoral Fellow

Van Vleck Visiting Assistant Professor

Contact info:

University of Wisconsin – Madison

Office: 809 Van Vleck

Phone: 608-262-3220

Email: hernandez at math dot wisc dot edu

Research area:

Applied Mathematics, Atmospheric Sciences

Numerical Analysis

Semiclassical Analysis

CV (Last updated: 09/08/13)

Future Conferences:

EMALCA (School of Mathematics of Latin America and the Caribbean) 2014 Chiapas, Mexico July 21

^{st}– August 1^{st}2014Summer School: UNAM – Querétaro Mexico June 23

^{rd}- 26^{th}2014SIAM Conference on NonLinear Waves and Coherent Structures, University of Cambridge, UK

Publications:

Turbulence:

*
G. Hernandez-Duenas, Leslie M. Smith, and Samuel N. Stechmann.
**Dissection
of Boussinesq nonlinear interactions using intermediate models.
**Journal
of Fluid Mechanics, 747 (2014), 247-287

Figure: Vertical vorticity of
dipole simulation by the P2G model

Atmospheric Sciences:

*
G. Hernandez-Duenas, Andrew J. Majda, Leslie M. Smith, and Samuel
N.
Stechmann. **Minimal
models for precipitating turbulent convection**
Journal
of Fluid Mechanics, 717 (2013), 576-611.

Figure:
Contours of rain water. Scattered convection (top) versus squall
lines (bottom).

**Hyperbolic
Conservation Laws:**

*
Jorge Balbás and G. Hernández-Dueñas. **A
Positivity Preserving Central Scheme for Shallow Water Flows in
Channels with Wet-Dry States.**
ESIAM: Mathematical Modelling and Numerical Analysis (M2AN) 48
(2014) 665-696.

Figure: Dam break simulation at different times. Blue: Water height. Brown: Bottom topography. Gray: Walls.

*
G. Hernández and Smadar Karni. **Shallow
Water Flows in Channels**.
J. Sci. Comput. 48 (2011), no. 1-3, 190-208.

Figure: Exact and numerical steady state (discontinuous transcritical) solutions to shallow water.

*
Smadar Karni and G. Hernández-Dueñas. **A
Hybrid Algorithm for the Baer-Nunziato Model Using the Riemann
Invariants.** J
Sci Comput, 45, (2010), 382-403.

Figure: Gas flow over a porous particle bed.

Figure: Solutions to the Baer-Nunziato system by a conservative formulation (left) and a hybrid formulation (right).

**Semiclassical
Analysis:**

*
G. Hernández-Dueñas and Alejandro Uribe. **Algebras
of semiclassical pseudodifferential operators associated with
Zoll-type domains in cotangent bundles**
(submitted).

Figure: Propagation of a coherent state in a Zoll-type domain.

**Proceedings:**

*
Smadar Karni and G. Hernández-Dueñas. **A
Hybrid Scheme for Flows in Porous Media**.
*Hyperbolic
Problems: Theory, Numerics, Applications*.
Proceedings of Simposia in Applied Mathematics, Volume 67, Part 2,
(2009), p 715-724. *Amer.
Math. Soc., Providence, RI, (2009).*

Figure:
Computed and exact solutions in a shock-tube problem using a
conservative (left) and a hybrid (right) formulation.

**Extended
abstracts:**

*
Smadar Karni and G. Hernández-Dueñas. **A
Scheme for Shallow Water Flow with Area Variation**.
American Institute of Physics. AIP Conference Proceedings,
International Conference on Numerical Analysis and Applied
Mathematics, Rethymno, Crete, Greece, 18-22 September 2009. 1168
(2009), p 1433-1436.

Figure: Schematic for the shallow water equations through rectangular channels with variable area.