Current and Former Students                                        (home)

Current Students

Vani Cheruvu, Postdoc, mentored jointly with Max Gunzburger and Lili Ju, October 2007 - present

Project Title: New Grid and Discretization Technologies for Ocean and Ice Simulations

Project Summary: The overarching purpose of this work is to determine how to resolve the critical aspects of ocean and ice systems while striving to improve computational efficiency. Thus, we strive to answer affirmatively the question: can grids be defined so that robust simulations of a desired accuracy can be obtained with less computational cost? or, stated more pragmatically, can we improve computational efficiency enough so that we can use an eddy-resolving ocean model in 100 year long IPCC coupled climate simulations? The tessellations we develop in this work, called Spherical Centroidal Voronoi Tessellations (SCVTs), are a superset of quasi-uniform grids that are now being widely used around the world. The tessellations are amenable to rigorous mathematical analyses, e.g., we know that our tessellations will become more uniform (and thus better) as the number of degrees of freedom increase.The tessellations are easy and straightforward to generate; it takes about 10 minutes on a PC to generate the eddy-resolving SCVT grid for the North Atlantic domain. Since numerical algorithms developed for uniform SCVT are applicable to nonuniform SCVTs, we will be able to quickly develop working models to test our nonuniform SCVTs while we continue to develop new, more refined, algorithms targeted to these nonuniform tessellations.

 

Former Students

Aarron Goldner, Summer Undergraduate Research Experience (SURE) student, June 2007 - August 2007.

Project Title: Bringing Climate Model Simulation Data into the GIS World

Project Summary: Data from climate model simulations are being increasingly used by those outside the field of climate modeling. Many of these new users of climate simulation data are interested in quantifying the regional impacts of anthroprogenic climate change. In these instances, climate data must be merged with other socio-economic data. A primary tool for organizing geospatial information for those outside the field of climate modeling is Geographical Information Systems (GIS). Unfortunately, climate model data is not commonly available in formats appropriate for GIS analysis. During the course of this project, data from the IPCC 4th Assessment Report was incorporated into the GRASS GIS framework. Extensions of this project include exporting the data into Google Earth KML format.

 

Matthew Dixon, Graduate Research Assistant, July 2006 - September 2006.

Project Title: A Variational Free-Lagrange Method for Shallow Water

Project Summary: Geometric numerical methods seek to transfer powerful theories in geometric mechanics to computational continuum dynamics. They preserve geometric structure in the flow field leading to excellent conservative properties. This property makes them attractive for climate modeling. For example, one can derive a geometric numerical method for the Lagrangian description of rotating shallow water equations which conserves mass, energy, potential vorticity and enstrophy. Lagrangian methods for hydrodynamics which describe the velocity field from particle positions and the density field with a moving mesh (with fixed connectivity) are not suited to long-time simulation of the climate because the mesh tangles. Moreover, rezoning and remapping techniques such as the alternating Eulerian-Lagrangian (ALE) method destroys the geometric structure of the flow field leading to poorer conservation properties.This work proposes to design a new Lagrangian method for rotating shallow water with bottom topography which has excellent conservative properties and is suitable for long-time simulation. The method is derived from a semi-discrete Hamilton's action principle to ensure preservation of geometric structure. The novel part is the use of a Voronoi diagram to represent the density field. This is dynamically reconstructed at each time step to avoid the tangling problem. Preliminary numerical results of long-time simulations confirm that this method conserves mass (locally) and energy. We close the talk with a discussion of potential vorticity conservation.