Page 9 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

Contents

1 Introduction .................................................... 1
1.1 Characteristics of Computational Geoscience . . . ................. 2
1.2 Basic Steps Associated with the Research Methodology
of Computational Geoscience . . . . . ............................ 3
1.2.1 The Conceptual Model of a Geoscience Problem . .......... 3
1.2.2 The Mathematical Model of a Geoscience Problem . . . ...... 3
1.2.3 The Numerical Simulation Model of a Geoscience Problem . . 4
1.2.4 Graphical Display of the Numerical Simulation Results . . . . . 5
1.3 The Contextual Arrangements of this Monograph ................. 5

2 A Progressive Asymptotic Approach Procedure for Simulating
Steady-State Natural Convective Problems in Fluid-Saturated
Porous Media ................................................... 7
2.1 Governing Equations of the Problem ............................ 9
2.2 Finite Element Formulation of the Problem ...................... 11
2.3 The Progressive Asymptotic Approach Procedure
for Solving Steady-State Natural Convection Problems
in Fluid-Saturated Porous Media . .............................. 14
2.4 Derivation of Analytical Solution to a Benchmark Problem . . . ...... 16
2.5 Verification of the Proposed Progressive Asymptotic Approach
Procedure Associated with Finite Element Analysis . . ............. 19
2.6 Application of the Progressive Asymptotic Approach Procedure
Associated with Finite Element Analysis ........................ 22
2.6.1 Two-Dimensional Convective Pore-Fluid Flow Problems . . . . 22
2.6.2 Three-Dimensional Convective Pore-Fluid Flow Problems . . . 28

3 A Consistent Point-Searching Interpolation Algorithm for
Simulating Coupled Problems between Deformation, Pore-Fluid
Flow, Heat Transfer and Mass Transport Processes in Hydrothemal
Systems ........................................................ 37
3.1 Statement of the Coupled Problem and Solution Method . .......... 38
3.2 Mathematical Formulation of the Consistent Point-Searching
Interpolation Algorithm in Unstructured Meshes ................. 42

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