Adaptive, Non-stiff, and Stochastic Methods for Phase Field Fluid Models

University Of California-Santa Barbara, Santa Barbara CA

Investigators

Abstract

The investigator proposes to develop innovative numerical methods for conservative phase field models of multi-phase and complex fluids. The new methods will becapable of resolving accurately and efficiently the disparate time and length scales involved in topological changes and complex interface morphologies, in the dynamics of the micro-scale structures, and in the effect of stochastic thermal fluctuations in phase transitions. Those capabilities will be obtained with novel space and time adaptive methods that take into account the mathematical structure and multi-scale nature of the models and their solutions. The methods will be designed to be free of high order stability constraints and will be of optimal computational cost. An effective, innovative coupling of stochastic and deterministic formulations is also proposed. Complex fluids found in a wide variety of industrial applications such as emulsions, foams, and polymeric solutions are characterized by multiple components, several coexisting phases, and structural heterogeneities spanning a broad range of length scales. The macroscopic behavior and properties of these fluid mixtures are a function of the intricate nonlinear coupling of the flow with micro- or nano- structures. The understanding of the dynamics of these systems is thus of significant scientific and technological interest. Computer simulation can play an instrumental role toward aiding in achieving this goal. The development of these numerical methods is the central objective of this proposal. The proposed research will be conducted in a multi-disciplinary environment and will also serve an important education goal: the interdisciplinary education and training of undergraduate and graduate students. An integral part of this project is also a sustained effort to promote and broaden the participation of underrepresented groups and the use of innovative pedagogic initiatives with ties with the industrial sector.