Abstract
We are interested in the numerical simulation of large scale phenomena in geophysical flows. In these cases, Coriolis forces play an important role and the circulations are often perturbations of the so-called geostrophic equilibrium. Hence, it is essential to design a numerical strategy that preserves a discrete version of this equilibrium. In this article we work on the shallow water equations in a finite volume framework and we propose a first step in this direction by introducing an auxiliary pressure that is in geostrophic equilibrium with the velocity field and that is computed thanks to the solution of an elliptic problem. Then the complete solution is obtained by working on the deviating part of the pressure. Some numerical examples illustrate the improvement through comparisons with classical discretizations.
Duc Nguyen
Associate Professor of Mathematics
Duc Nguyen develops mathematical and AI frameworks for molecular bioscience, drug discovery, and scientific computing. His group blends differential geometry, graph theory, and machine learning to build high-fidelity models for biomolecular systems, with notable wins in the D3R Grand Challenges and collaborations with Pfizer and Bristol Myers Squibb. Supported by multiple NSF awards, he has advised students and postdocs across theory and applications of AI-driven drug design.