Fast Spectral-Galerkin Methods and Their Applicatons

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The PI will develop and analyze fast and accurate spectral methodsfor solving a large class of partial differential equations and applythem to investigate several important problems of current interest,including in particular the inter-facial dynamics of multiphase complexflows, stability and dynamics of stratified shear flows andmicro-structural evolutions in advanced materials processing. Theproposed research will result in fast and accurate numericalalgorithms which will allow simulations of three-dimensionaltime-dependent problems within a reasonable turn-over time, andprovide capabilities to numerically attack challenging problemsarising from emerging engineering and scientific applications.As computer simulations are playing an ever increasing role in manybranches of science and engineering and are rapidly replacing much ofthe expensive prototyping and testing phases in manufacturing and inscience explorations, fast and robust numerical methods are becomingan indispensable tool for many scientists and engineers, especiallyfor computational scientists in fluid dynamics and materials science.It is expected that our numerical simulations will contribute towardsbetter understandings of the complex physical and mathematicalproblems, and provide valuable information for the designs of advancedmaterials and of a space experiment on stratified shear flows.