Computational upscaled modeling of heterogeneous porous media flow utilizing finite volume method
In this dissertation we develop and analyze numerical method to solve general elliptic boundary value problems with many scales. The numerical method presented is intended to capture the small scales e?ect on the large scale solution without resolving the small scale details, which is done through the construction of a multiscale map. The multiscale method is more e?ective when the coarse element size is larger than the small scale length. To guarantee a numerical conservation, a ?nite volume element method is used to construct the global problem. Analysis of the multiscale method is separately done for cases of linear and nonlinear coe?cients. For linear coe?cients, the multiscale ?nite volume element method is viewed as a perturbation of multiscale ?nite element method. The analysis uses substantially the existing ?nite element results and techniques. The multiscale method for nonlinear coe?cients will be analyzed in the ?nite element sense. A class of correctors corresponding to the multiscale method will be discussed. In turn, the analysis will rely on approximation properties of this correctors. Several numerical experiments verifying the theoretical results will be given. Finally we will present several applications of the multiscale method in the ?ow in porous media. Problems that we will consider are multiphase immiscible ?ow, multicomponent miscible ?ow, and soil in?ltration in saturated/unsaturated ?ow.
Advisor:Lazarov, Raytcho; Efendiev, Yalchin; Datta-Gupta, Akhil; Pasciak, Joseph; Ewing, Richard
School:Texas A&M University
School Location:USA - Texas
Source Type:Master's Thesis
Keywords:multiscale modeling heterogeneous media finite volume numerical homogenization porous flow macro diffusion model
Date of Publication:05/01/2003