CIMMS Focused Workshop on
Multiscale Techniques for Dynamic Interfaces

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WELCOME
to the CIMMS Workshop on "Multiscale Techniques for Dynamic Interfaces"

The problem of modeling interface dynamics has been receiving a great deal of attention in recent years by a wide variety of different groups. Level set and phase field methods are just a few of the techniques that have been employed to simulate complicated fluid motion, wherein topological changes in the interface may occur, e.g., wave breaking, droplets, spray, coalescence, etc.

The mathematical analysis of these modeling techniques is just beginning and a number of fundamental questions remain open. Traditional continuum models may break down when topological transions take place. New multiscale or multi-level models need to be introduced to supplement the existing continuum models to capture the correct multiscale physics near the topological singularity. Furthermore, sharp interface methods such as traditional level set techniques, must be regularized (in some fashion) in order to evolve interfaces past singularities; do such regularizations converge?

Viscosity solutions, developed for phase transitions in materials, such as for the Allen-Cahn-type models, are NOT known to work in the fluids setting because maximum principles for derivatives are lost due to the presence of coupling terms, which are usually the advection terms. On the other hand, phase field models, which can be shown to have weak convergence properties, require adaptive mesh refinement in the the diffuse interface transition zone, and thus may be computationally expensive.

This workshop would like to address these important issues, and try to develop a consensus from the community of researchers as to the most important future avenues of research, from a mathematical, computational, and physical perspective.

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