Event Detail

Event Type: 
Tuesday, May 17, 2022 - 09:30 to 11:30
Valley Library Willamette West Seminar Room

In this dissertation, we discuss mathematical and computational models for phase change at multiple scales. We focus on two scales: the porescale and the Darcy scale, both relevant for porous media models. We consider two applications: (1) ice-water phase transitions in the presence of grains at porescale, with applications to permafrost modeling, and (2) modeling microbial growth forming phase, with applications in porous media. We also provide a broader context of literature on phase change, phase mixing and phase separation models as well as variational inequalities and illustrate these with simulations, some in complicated porescale geometries.

The first model (1) is a nonlinear heat conduction model which features a free boundary. We focus on the mathematical and computational challenges associated with the nonlinear and discontinuous character of constitutive relationships related to the presence of free boundaries and material interfaces. We use monolithic
discretization framework based on lowest order mixed finite elements on rectangular grids well known for its conservative properties. We implement this scheme as cell centered finite differences, and combine with a fully implicit time stepping scheme. We show that our algorithm is robust and compares well to known approaches. Next we extend these algorithms to the heterogeneous case. We also connect the porescale model to Darcy scale by upscaling and compare to the empirical permafrost models known from literature.

The biofilm model (2) describes the microbial growth as well as nutrient utilization. As with the heat conduction model, we show our entire model is monolithic and robust computationally even in complex pore-scale geometries.