Higher-order, strongly stable methods for uncoupling groundwater-surface water flow.

摘要

Many environmental problems today involve the prediction of the migration of contaminants in groundwater-surface water flow. Sources of contaminated groundwater-surface water flow include: landfill leachate, radioactive waste from underground storage containers, and chemical run-off from pesticide usage in agriculture, to name a few. Before we can track the transport of pollutants in environmental flow, we must first model the flow itself, which takes place in a variety of physical settings. This necessitates the development of accurate numerical models describing coupled fluid (surface water) and porous media (groundwater) flow, which we assume to be described by the fully evolutionary Stokes-Darcy equations. Difficulties include finding methods that converge within a reasonable amount of time, are stable when the physical parameters of the flow are small, and maintain stability and accuracy along the interface. Ideally, because there exist a wide variety of physical scenarios for this coupled flow, we desire numerical methods that are versatile in terms of stability and practical in terms of computational cost and time.;The approach to model this flow studied herein seeks to take advantage of existing efficient solvers for the separate sub-flows by uncoupling the flow so that at each time level we may solve a separate surface and groundwater problem. This approach requires only one (SPD) Stokes and one (SPD) Darcy sub-physics and sub-domain solve per time level for the time-dependent Stokes-Darcy problem. In this dissertation, we investigate several different methods that uncouple groundwater-surface water flow, and provide thorough analysis of the stability and convergence of each method along with numerical experiments.