Van Vleck Visiting Assistant Professor
University of Wisconsin – Madison
Department of Mathematics
Office: 809 Van Vleck
Email: hernandez at math dot wisc dot edu
Applied Mathematics, Atmospheric Sciences
CV (Last updated: 09/08/13)
EMALCA (School of Mathematics of Latin America and the Caribbean) 2014 Chiapas, Mexico July 21st – August 1st 2014
Summer School: UNAM – Querétaro Mexico June 23rd - 26th 2014
SIAM Conference on NonLinear Waves and Coherent Structures, University of Cambridge, UK
* 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
* 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).
* 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.
* 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.
* 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.