Page 7 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

viii Preamble
for natural mineral resources, computational geoscience has achieved much in the
past decade, driven from the need to understand controlling mechanisms behind
ore body formation and mineralization in hydrothermal systems within the upper
crust of the Earth. In order to disseminate widely the existing knowledge of com-
putational geoscience, to promote extensively and fastly further development of the
computational geoscience, and to facilitate efficiently the broad applications of com-
putational geoscience, it is high time to publish a monograph to report the current
knowledge in a systematic manner. This monograph aims to provide state-of-the-
art numerical methods, procedures and algorithms in the field of computational
geoscience, based on the authors’ own work during the last decade. For this pur-
pose, although some theoretical results are provided to verify numerical ones, the
main focus of this monograph is on computational simulation aspects of this newly-
developed computational geoscience discipline. The advanced numerical methods,
procedures and algorithms contained in this monograph are also applicable to a
wide range of problems of other length-scales such as engineering length-scales.
To broaden the readership of this monograph, common mathematical notations are
used to describe the theoretical aspects of geoscience problems. This enables this
monograph to be used either as a useful textbook for postgraduate students or as
an indispensable reference book for computational geoscientists, mathematicians,
engineers and geoscientists. In addition, each chapter is written independently of
the remainder of the monograph so that readers may read the chapter of interest
separately.
In this monograph we use the finite element method, the finite difference
method and the particle simulation method as basic numerical methods for deal-
ing with geoscience problems. Not only have these three methods been well de-
veloped in the field of computational science, but also they have been successfully
applied to a wide range of small-scale scientific and engineering problems. Based
on these three methods, we have developed advanced numerical procedures and
algorithms to tackle the large-scale aspects of geoscience problems. The specific
geoscience problem under consideration is the ore body formation and mineraliza-
tion problem in hydrothermal systems within the upper crust of the Earth. Towards
this end, we present the advanced procedures and algorithms in this monograph
as follows: (1) Due to the important role that convective pore-fluid flow plays in
the controlling processes of ore body formation and mineralization, a progressive
asymptotic approach procedure is proposed to solve steady-state convective pore-
fluid flow problems within the upper crust of the Earth. (2) To consider both the
thermoelastic effect and the double diffusion effect, a consistent point-searching
interpolation algorithm is proposed to develop a general interface between two com-
mercial computer codes, Fluid Dynamics Analysis Package (FIDAP) and Fast La-
grangian Analysis of Continua (FLAC). This general interface allows a combination
use of the two commercial codes for solving coupled problems between medium
deformation, pore-fluid flow, heat transfer and reactive mass transport processes
that can occur simultaneously in hydrothermal systems. (3) To simulate mineral
dissolution/precipitation and metamorphic processes, a term splitting algorithm is
developed for dealing with fluid-rock interaction problems in fluid-saturated hy-