Gerardo Hernández - Dueñas RESEARCH STATEMENT IN : NUMERICAL ANALYSIS
نویسنده
چکیده
My research interests include the areas of numerical methods for hyperbolic conservation laws, shallow water flows, fluid dynamics, flows in porous media and multi-phase flows. Here I explain the contributions I have made to numerical analysis, in collaboration with Professor Smadar Karni. However, I also enjoy working on semiclassical analysis, which has been a parallel project in my doctoral dissertation. In collaboration with Professor Alejandro Uribe, we have made contributions to the quantization of some symplectic manifolds with boundary, and developed a symbolic calculus for pseudodifferential operators with singular symbols. This has applications to spectral theory and mathematical physics. My research statement of that area is available on my webpage:
منابع مشابه
Hernández - Dueñas RESEARCH STATEMENT IN : SEMICLASSICAL ANALYSIS
My research interests include the area of semiclassical analysis. In collaboration with Professor Alejandro Uribe, we develop semiclassical analysis on certain phase spaces (symplectic manifolds) with boundary, construct a symbolic calculus for semiclassical operators with singular symbols and study propagation. This has applications to spectral theory and mathematical physics. However, I also ...
متن کاملA Hybrid Scheme for Flows in Porous Media
Abstract. The Baer-Nunziato model is used to describe the flow of compressible gas in a porous bed. We are concerned with flows in which the porosity changes discontinuously across a so-called compaction wave, and consider the related Riemann problem. A recent study [CAL] has illustrated the failure of various numerical schemes to compute correct solutions across compaction waves. The errors we...
متن کاملMinimal models for precipitating organized convection
GERARDO HERNÁNDEZ-DUEÑAS, ANDREW J. MAJDA, LESLIE M. SMITH AND SAMUEL N. STECHMANN †, Department of Mathematics, University of Wisconsin–Madison, Madison, WI 53706, USA 2 Department of Mathematics and Center for Atmosphere-Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, NY Department of Engineering Physics, University of Wisconsin–Madison, Madison, WI 5...
متن کاملShallow Water Flows in Channels
We consider the shallow water equations for flows through channels with arbitrary cross-section. The system forms a hyperbolic set of balance laws. Exact steady-state solutions are available and are controlled by the relation between the bottom topography and the channel geometry. We use a Roetype upwind scheme for the system. Considerations of conservation, near steady-state accuracy, velocity...
متن کاملA Hybrid Algorithm for the Baer-Nunziato Model Using the Riemann Invariants
The paper considers the Baer-Nunziato model for two-phase flow in porous media, with discontinuous porosity. Computing solutions of the Riemann problem rests on capturing the jump in the solution across the porosity jump. A recent study [8] showed that numerical discretizations may fail to correctly capture the jump conditions across the so-called compaction wave, and yield incorrect solutions....
متن کامل