Modelling Surface and Sub-Surface Flows

Modelling Surface and Sub-Surface Flows.

Finite Element Simulation in Surface and Subsurface Hydrology provides an introduction to the finite element method and how the method is applied to problems in surface and subsurface hydrology. The book presents the basic concepts of the numerical methods and the finite element approach; applications to problems on groundwater flow and mass and energy transport; and applications to problems that involve surface water dynamics. Computational methods for the solution of differential equations; classification of partial differential equations; finite difference and weighted residual integral techniques; and The Galerkin finite element method are discussed as well. The text will be of value to engineers, hydrologists, and students in the field of engineering.

Research works on the coupling of incompressible surface flow with subsurface porous media flow arouse increasing interest recently. The coupled problem is a typical multi-domain problem with multi-physics. In-depth understanding of this problem requires both modeling process and numerical study. In this work, some existing surface flow models and subsurface flow models are reviewed; the interaction mechanisms of surface flow with subsurface porous media flow are discussed; numerical algorithms for solving coupled surface/subsurface flow models are proposed; in particular, preconditioning techniques and two grid algorithms are mathematically and numerically investigated. In Chapter 1, we present some existing models for describing surface fluid flow motion as well as those for subsurface porous media flow motion. Moreover, we study some coupled models including both surface fluid flow and subsurface porous media flow. The interactions of fluid flow and porous media flow are reflected by transmission conditions at the interface between surface and subsurface. Other related multimodels for incompressible flows will also be introduced. In Chapter 2, we focus on preconditioning techniques for the coupled Stokes/Darcy model, a linear model for the surface/subsurface flows coupling. Several decoupled preconditioners are proposed and analyzed. Especially, the convergence rate of GMRES method with these preconditioners is shown to be independent of meshsize. For improving the robustness with respect to physical parameters, coupled preconditioners are also theoretically and numerically investigated. In Chapter 3, a two grid algorithm for decoupling the coupled Stokes/Darcy model is studied. The two grid algorithm consists of solving a coupled coarse grid problem, then solving two sub-problems in parallel. We use coarse grid solution to supplement boundary conditions at the interface for fine grid subproblems. Theoretical analysis shows that the two grid algorithm retains opt.

Describes fluid flow, transport and contamination in rocks and sediments, for graduate students and professionals in hydrology, water resources, geochemistry.