Stefanie Fazekas' presentation

TITLE: Mathematical and Computational Aspects for Two Flow Models in the Cascades

ABSTRACT: In this talk we will discuss the mathematical and computational aspects of two different water flow models. The first model couples a Darcy flow with heat conduction. This model allows us to study the pressure, flux, and temperature of water seeping through porous media such as soil or snow. The second model describes an unsaturated nonlinear flow. This model allows us to measure the water saturation as water seeps downward through a layer of snow.

Bailey Sharon's presentation

TITLE: Mathematical Models and Computational Examples Coupling Channel Network and Groundwater Flow with Beaver Influence

ABSTRACT: We present a flexible numerical model that couples a one-dimensional channel network with a two-dimensional groundwater flow model to examine interactions between surface and subsurface domains. The model applies pressure coupling conditions to spatially overlapping unknowns to simulate flux exchange and evaluate the hydrological impact of beaver-made structures on flow dynamics. Surface flow is represented using an edge-node incidence matrix, and the subsurface domain is discretized using a cell-centered finite difference method. Coupling is performed using both monolithic and iterative approaches to balance efficiency and adaptability in complex systems. Numerical examples show that the introduction of beaver-made structures alters pressure distributions in both domains by stabilizing upstream surface pressures and increasing subsurface flow. These findings provide a mathematical framework for understanding the impact of surface modifications on subsurface hydrology, offering insights into the design and placement of beaver-made structures during wetland restoration.