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Design and Analysis of Numerical Schemes with Characteristic Methods on Generic Grids for Flows in Porous Media

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thesis
posted on 16.08.2019, 00:25 by HANZ MARTIN CHENG
This thesis studies characteristic-based numerical schemes for a mathematical model of miscible fluid flow in porous media, a coupled and advection-dominated system of partial differential equations describing an oil recovery process. In particular, we analyse characteristic-based schemes on generic polygonal meshes, with diffusive component discretised using modern finite volume methods. We also develop a novel algorithm for reconstructing velocity fields suitable for characteristic tracking. The proposed scheme mixes two characteristic-based discretisations, and implements an original post-processing algorithm to ensure local and global mass conservation. Extensive numerical tests are provided, on various polygonal meshes. A rigorous convergence analysis is also performed.

History

Campus location

Australia

Principal supervisor

Jerome Droniou

Year of Award

2019

Department, School or Centre

Mathematical Sciences

Course

Doctor of Philosophy

Degree Type

DOCTORATE

Faculty

Faculty of Science Theses