Gerardo Hernández Dueñas

My name in papers appears as:

Gerardo Hernandez-Duenas

Institute of Mathematics - UNAM Juriquilla

See other campuses:

Institute of Mathematics - UNAM Mexico City

Institute of Mathematics - UNAM Cuernavaca

Institute of Mathematics - UNAM Oaxaca

Hyperbolic Conservation Laws:

(*) A central-upwind scheme with artificial viscosity for shallow-water flows in channels.

G. Hernandez-Duenas and Abdelaziz Beljadid.

Advances in Water Resources 96 (2016) 323-338.

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Figure (left): Schematic of channel in numerical experiment of dam break

Figure (right): Comparison with experimental data

(*) A Positivity Preserving Central Scheme for Shallow Water Flows in Channels with Wet-Dry States.

Jorge Balbás and G. Hernandez-Duenas. 

ESIAM: Mathematical Modelling and Numerical Analysis (M2AN) 48 (2014) 665-696.

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

(*) Shallow Water Flows in Channels.

G. Hernandez-Duenas and Smadar Karni.

J. Sci. Comput. 48 (2011), no. 1-3, 190-208.

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

(*) A Hybrid Algorithm for the Baer-Nunziato Model Using the Riemann Invariants.

Smadar Karni and G. Hernandez-Duenas.

J Sci Comput, 45, (2010), 382-403.

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Figure 1: Schematic: Gas flow over a porous particle bed.

Figure 2: Solutions to the Baer-Nunziato system by a conservative formulation (left) and a hybrid formulation (right).

Semiclassical Analysis:

(* )Algebras of semiclassical pseudodifferential operators associated with Zoll-type domains in cotangent bundles

G. Hernandez-Duenas and Alejandro Uribe.

Journal of Functional Analysis, 268 no. 7 (2015), pp. 1755-1807

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

Atmospheric Sciences:

(*) Stability and instability criteria for idealized precipitating hydrodynamics

G. Hernandez-Duenas, Leslie M. Smith, and Samuel N. Stechmann.

Journal of Atmospheric Sciences, Vol 72, No. 6 (2015), pp. 2379-2393

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Figure: Growth rates versus horizontal wavenumbers for different values of rainfall speed.

(*)  Minimal models for precipitating turbulent convection

G. Hernandez-Duenas, Andrew J. Majda, Leslie M. Smith, and Samuel N. Stechmann.

Journal of Fluid Mechanics, 717 (2013), 576-611.

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Figure: Contours of rain water. Scattered convection (left) versus squall lines (right).

Turbulence:

(*) Investigation of Boussinesq dynamics using intermediate models based on wave-vortical interactions.

G. Hernandez-Duenas, Leslie M. Smith, and Samuel N. Stechmann

Journal of Fluid Mechanics, 747 (2014), 247-287

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Ph.D.Thesis (University of Michigan - Ann Arbor):

(*) Numerical Methods for Porous Media and Shallow Water Flows & An Algebra of Singular Semiclassical Pseudodifferential Operators

G. Hernandez-Duenas.

Proceedings:

(*) A Hybrid Scheme for Flows in Porous Media.

Smadar Karni and G. Hernandez-Duenas.

Hyperbolic Problems: Theory, Numerics, Applications.

Proceedings of Simposia in Applied Mathematics, Volume 67, Part 2, (2009), 715-724.

Amer. Math. Soc., Providence, RI, (2009).

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

Extended abstracts:

(*) A Scheme for Shallow Water Flow with Area Variation.

Smadar Karni and G. Hernandez-Duenas.

American Institute of Physics.

AIP Conference Proceedings

International Conference on Numerical Analysis and Applied Mathematics

Rethymno, Crete, Greece, 18-22 September 2009. 1168 (2009), 1433-1436.

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