Page 6 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

Preamble

In recent years, numerical methods and computational simulations provide a new
way to deal with many geoscience problems, for which the traditionally-used the-
oretical and experimental methods may not be valid as a result of the large time
and length scales of the problems themselves. This enables many hitherto unsolv-
able geoscience problems to be solved using numerical methods and computational
simulations. In particular, through wide application of computational science to
geoscience problems, a new discipline, namely computational geoscience, has been
established. However, because of the extremely large length and time scales, the
numerical simulation of a real geological world also provides many challenging
problems for researchers involved in the field of computational science. For this
reason, multidisciplinary knowledge and expertise from mathematicians, physicists,
chemists, computational scientists and geoscientists are required in the process of
establishing the research methodology of computational geoscience.
Since computational geoscience is an amalgamation of geoscience and com-
putational science, theoretical analysis and computational simulation are two of its
core members. On the theoretical analysis front, we need: (1) to measure and gather
data and information through traditional geoscience observations and measurements
such as those widely used in geology, geophysics, geochemistry and many other
scientific and engineering fields; (2) to conduct research to find the key factors and
processes that control the geoscience problem under consideration; (3) to establish
the theoretical foundations of the geoscience problem through formulating a set
of partial differential equations on the basis of fundamental scientific principles;
(4) to investigate the solution characteristics of these partial differential equations
using rigorous mathematical treatments. On the computational simulation front, we
need: (1) to develop advanced numerical methods, procedures and algorithms for
simulating multi-scale and multi-process aspects of the geoscience problem on the
basis of contemporary computational science knowledge and expertise; (2) to verify
computational codes established on the basis of these advanced numerical meth-
ods, procedures and algorithms through comparing numerical solutions with bench-
mark solutions; (3) to produce and validate numerical solutions of real geoscience
problems.
Owing to the broad nature of geoscience problems, computational geoscience
is at a developing stage. Nevertheless, under the stimulus of ever-increasing demand

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