Discretizing the flow equation

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Table of contents

Abstract
Acknowledgement
List of Figures
List of Tables
Nomenclature
Thesis outline
Governing equations
Single-phase flow
Multiphase flow
Pressure equation
Saturation equation
Literature review
Stochastic approaches
Numerical methods
Finite difference and finite volume methods
Finite element and discontinuous Galerkin methods
Flow diagnostic tools
Upscaling
Single-phase upscaling
Multiphase upscaling
Alternative approaches
Dual grid techniques
Multiscale methods
Adaptive gridding
Localization of the saturation discontinuity
Front tracking methods
Level set method
Fast marching method
Discretization methods
Finite volume method
Single-phase flow
Multiphase flow
Numerical errors
Discontinuous Galerkin method
Discretizing the flow equation
Adaptation of FESTUNG for reservoir simulations
Reconstruction of conservative fluxes
Using the underlying permeability values
Numerical errors
Fast front tracking method
Buckley Leverett problem
FFrT formulation
Test case validation
Buckley Leverett problem
Layered medium
Random generated isotropic medium
SPE10 benchmark test
Combining FFrT with adaptive coarsening: A proposed approach for immiscible multiphase flows
Formulation
Complexity analysis
Numerical examples
Numerical example one: Pressure solution on the base coarse grid
Numerical example two: Adaptive coarsening criterion
Numerical example three: Domain decomposition
Numerical example four: Non-uniform coarsening
Numerical example five: Intermediate resolution level
Numerical example six: Favourable displacement
Numerical example seven: Unfavourable displacement
Conclusion
Concluding remarks
Future work
References