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# Steve Wise (University of Tennessee, Knoxville), Applied Mathematics Colloquium

## March 24, 2017 @ 4:00 pm - 5:00 pm

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**Title: **Diffuse Interface Models of Multi-Phase Flows with Large Density Contrast and their Efficient Approximation with Adaptive Multigrid Methods

**Abstract: **In many fluid flow problems, two or more constituents are fully or partially immiscible, leading to multiple phases separated by interfaces. Of these, several have the additional property that at least one of the phases has a mass density that is significantly larger or smaller than the others. I will describe two problems of this type, one coming from the evaporation of a solvent in the processing of multi-phase polymer mixtures in an organic photovoltaic (OPV) application and another from simpler two-phase flows. There are many ways to build models of these phenomena. I will develop the OPV equations using the theory of mixtures, using a volume fraction approach. All of the models that I will investigate are of the diffuse interface type, wherein interfaces are approximated with a larger-than-physical interfacial thickness via an order parameter. The utility of the approach is that one does not have to explicitly track the dynamics of the interfaces. On the other hand, one does need to resolve time-evolving fields with large gradients. In the latter part of the talk, time permitting, I will describe efficient adaptive nonlinear multigrid methods for efficiently solving the model equations. I will focus on some recent advances in the adaptive algorithms for seamlessly incorporating mass conservation.