Page 17 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

1.2 Basic Steps Associated with the Research Methodology of Computational Geoscience 3
1.2 Basic Steps Associated with the Research Methodology
of Computational Geoscience

Generally speaking, the research methodology of computational geoscience is a
comprehensive research methodology, which is formed by combining field obser-
vation, theoretical analysis, numerical simulation and field validation. The pri-
mary aim of using this research methodology is to investigate the dynamic pro-
cesses and mechanisms involved in an observed geological phenomenon, rather than
to describe the observed geological phenomenon itself. The appropriate research
methodology of computational geoscience is usually comprised of the following
four main steps: (1) the establishment of a conceptual model for a given geoscience
problem; (2) the establishment of a mathematical model for the given problem; (3)
the construction of a numerical simulation model for the given problem and (4) the
graphical display of the numerical results obtained from the numerical simulation.

1.2.1 The Conceptual Model of a Geoscience Problem

Based on extensive data and information obtained from field and laboratory inves-
tigations of a geological phenomenon, a conceptual model is established, which
reflects the geometrical architecture and main processes associated with the phe-
nomenon. This is the key step in the process of using the research methodology of
computational geoscience to solve a problem. Due to the multiple processes and
multiple scales involved in a typical geoscience problem, only the major control-
ling dynamic processes and mechanisms associated with the problem need to be
considered during the initial establishment of the conceptual model. Since other
unimportant, or at least less critical, processes and factors are neglected, the initial
conceptual model of the problem is somewhat simplified. This conceptual model is
used to represent the main characteristics of the real geoscience problem. As under-
standing grows more detail may be added if necessary.
The fundamental principle involved in establishing the conceptual model for the
problem is that the details of the conceptual model should depend on both the length-
scale and time-scale of the problem. The conceptual model cannot be over simpli-
fied, since then it cannot be used effectively to reflect the main dynamic processes
and mechanisms of the real problem. On the other hand, the conceptual model can-
not be over complicated, for then unnecessary problems for both the theoretical anal-
ysis and the numerical simulation may arise and it may become difficult to unravel
which parts of the description of the problem are important.

1.2.2 The Mathematical Model of a Geoscience Problem

Using three fundamental principles, namely the conservation of mass, the conser-
vation of momentum and the conservation of energy, as well as the related physical
and chemical laws (Bear 1972, Bear and Bachmat 1990, Phillips 1991, Nield and
Bejan 1992, Zhao et al. 1997a), the conceptual model for the given problem can be