Page 19 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

1.3 The Contextual Arrangements of this Monograph 5

designed for solving engineering problems, cannot be directly used to solve geo-
science problems without modification. For this reason, it is necessary either to
develop new computer programs for solving geoscience problems or to modify the
existing commercial computer programs, originally designed for solving engineer-
ing problems, so as to be suitable for these problems.
It is noted that the solution reliability of a geoscience problem is strongly depen-
dent on algorithm convergence, algorithm stability, mesh shape, time-step and other
factors. To ensure the accuracy and reliability of the computational simulation result
for a problem, the above-mentioned factors need to be carefully considered in the
process of establishing the computational simulation model. A newly-developed
computer program needs to be verified through the corresponding benchmark prob-
lem before it is used to solve any real geoscience problems. Otherwise, the reliabil-
ity of the numerical solution obtained from a newly-developed computer program
cannot be guaranteed.

1.2.4 Graphical Display of the Numerical Simulation Results

The numerical results obtained from the computer simulation of a geoscience prob-
lem are expressed as a large amount of data, which can be viewed using modern
technologies of computer graphical display. By comparing the numerical solution
with field observations of the geological phenomenon, the correctness of the estab-
lished conceptual model for the geoscience problem can be tested. Thus the research
methodology of computational geoscience is firstly established on the basis of field
observations, and then goes through theoretical analysis and computational simula-
tion. Finally the results must be tested through comparison with existing or new field
observations. This fundamental research methodology requires that the recognition
of a natural phenomenon start from field observations, and be completed through
further tests arising from field observations, resulting in a circular iteration.
If the numerical solution is not compatible with the field observations, then the
established conceptual model of the problem is questionable and therefore needs
to be modified through further refinement of the natural data. On the contrary, if
the numerical solution is in accord with the field observations, then the established
conceptual model of the geoscience problem is a reasonable interpretation of what
may have occurred in nature. In this case, the established conceptual model of the
geoscience problem can be further used to investigate the fundamental rules asso-
ciated with this kind of problem. In this regard, the research methodology of com-
putational geoscience can provide an effective scientific-judging method for solving
many controversial problems in the field of geoscience.

1.3 The Contextual Arrangements of this Monograph

In this monograph we use the finite element method, the finite difference method
and the particle simulation method as basic numerical methods for dealing with
geoscience problems. Based on these three methods, we have developed advanced