Simulation

Novel methods for the computationally efficient simulation of compressible fluid flow will be developed, with applications to aerospace and space physics. First, new formulations of multigrid techniques for the implicit solution of time-dependent flows will be studied, using parabolization to increase diagonal dominance and solution efficiency. Second, new direct solution methods for steady transonic flows will be developed, employing dynamical systems and characteristic analysis.

With today’s rapidly increasing energy demands and the emergence of smart grids and renewable energy resources, the current energy and power technologies need to be advanced to keep up with these changes. Simulation and modeling plays a vital role in understanding, designing and planning of electrical power systems. The proposed research aims at developing a new generation of advanced mathematical models and simulation tools for electrical power systems and smart grids.

Coherent Anti-Stokes Raman Scattering (CARS) microscopy is a very promising method of directly imaging biological processes occurring in living cells. It is unique because the imaging does not harm the cell, is molecule specific, and does not require the introduction of additional chemicals that may alter the biology. For example, CARS would allow us to visualize how viruses invade a cell membrane, which is still a mystery.

Many fundamental and important scientific and industrial processes can be described in terms of transport phenomena, or processes in which particles are physically displaced from one location to another. Transport phenomena are broadly categorized into three types: transport of mass, transport of energy and transport of momentum.