The PI will develop and analyze fast and accurate spectral methods for solving a large class of partial differential equations and apply them to investigate several important problems of current interest, including in particular the inter-facial dynamics of multiphase complex flows, stability and dynamics of stratified shear flows and micro-structural evolutions in advanced materials processing. The proposed research will result in fast and accurate numerical algorithms which will allow simulations of three-dimensional time-dependent problems within a reasonable turn-over time, and provide capabilities to numerically attack challenging problems arising from emerging engineering and scientific applications.
As computer simulations are playing an ever increasing role in many branches of science and engineering and are rapidly replacing much of the expensive prototyping and testing phases in manufacturing and in science explorations, fast and robust numerical methods are becoming an indispensable tool for many scientists and engineers, especially for computational scientists in fluid dynamics and materials science. It is expected that our numerical simulations will contribute towards better understandings of the complex physical and mathematical problems, and provide valuable information for the designs of advanced materials and of a space experiment on stratified shear flows.
