Page 10 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

xii Contents

3.2.1 Point Searching Step . . . . . . ............................ 43
3.2.2 Inverse Mapping Step . . . . . . ............................ 45
3.2.3 Consistent Interpolation Step ........................... 50
3.3 Verification of the Proposed Consistent Point-Searching
Interpolation Algorithm ...................................... 51
3.4 Application Examples of the Proposed Consistent Point-Searching
Interpolation Algorithm ...................................... 56
3.4.1 Numerical Modelling of Coupled Problems Involving
Deformation, Pore-Fluid Flow and Heat Transfer
in Fluid-Saturated Porous Media ........................ 56
3.4.2 Numerical Modelling of Coupled Problems Involving
Deformation, Pore-Fluid Flow, Heat Transfer and Mass
Transport in Fluid-Saturated Porous Media . .............. 59

4 A Term Splitting Algorithm for Simulating Fluid-Rock Interaction
Problems in Fluid-Saturated Hydrothermal Systems of Subcritical
Zhao Numbers .................................................. 73
4.1 Key Issues Associated with the Numerical Modelling of Fluid-Rock
Interaction Problems......................................... 76
4.2 Development of the Term Splitting Algorithm . . . ................. 77
4.3 Application Examples of the Term Splitting Algorithm . . .......... 82

5 A Segregated Algorithm for Simulating Chemical Dissolution Front
Instabilities in Fluid-Saturated Porous Rocks ....................... 95
5.1 Mathematical Background of Chemical Dissolution Front
Instability Problems in Fluid-Saturated Porous Rocks ............. 96
5.1.1 A General Case of Reactive Multi-Chemical-Species
Transport with Consideration of Porosity/Permeability
Feedback . .......................................... 96
5.1.2 A Particular Case of Reactive Single-Chemical-Species
Transport with Consideration of Porosity/Permeability
Feedack. . . .......................................... 99
5.2 Proposed Segregated Algorithm for Simulating the Morphological
Evolution of a Chemical Dissolution Front ...................... 109
5.2.1 Formulation of the Segregated Algorithm for Simulating
the Evolution of Chemical Dissolution Fronts ............. 109
5.2.2 Verification of the Segregated Algorithm for Simulating
the Evolution of Chemical Dissolution Fronts ............. 111
5.3 Application of the Segregated Algorithm for Simulating
the Morphological Evolution of Chemical Dissolution Fronts . ...... 115