Page 73 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

3.4 Examples of the Proposed Consistent Point-Searching Interpolation Algorithm 59

well distributed anti-symmetrically. This indicates that the vertical forces are well
balanced in the horizontal cross-section of the computational domain.

3.4.2 Numerical Modelling of Coupled Problems Involving
Deformation, Pore-Fluid Flow, Heat Transfer and Mass
Transport in Fluid-Saturated Porous Media

Generally, the numerical algorithms and methods can be used to answer many what-
if questions related to ore body formation and mineralization that can be described
as coupled problems between medium deformation, pore-fluid flow, heat transfer
and reactive mass transport in fluid-saturated porous media. However, due to the
approximate nature of a numerical solution, it is essential to evaluate the accuracy
of the numerical solution, at least qualitatively if the analytical solution to the prob-
lem is not available. This requires us to have a strong theoretical understanding of
the basic governing principles and processes behind the coupled problem. Specifi-
cally, we must know, through some kind of theoretical analysis, what the pore-fluid
can and cannot do, and what reaction patterns the reactive pore-fluid can produce
in a hydrothermal system. For this reason, we have been making efforts, in recent
years, to develop theoretical solutions to verify the numerical methods developed
(Zhao and Valliappan 1993a, b, 1994a, b, Zhao et al. 1997a, 1998a, 1999b). On
the other hand, a good numerical solution can provide insights into the integrated
behaviour of different processes that occur in a hydrothermal system. Even in some
circumstances, a good numerical solution can provide some useful hints for deriving
analytical solutions to some aspects of the problem. This indicates that the numerical
and theoretical approaches are, indeed, complementary in the field of computational
geoscience. Realizing this particular relationship between the analytical method and
the numerical method, Phillips (1991) stated that: “A conceptual framework eluci-
dating the relations among flow characteristics, driving forces, structure, and reac-
tion patterns enables us not only to understand the results of numerical modelling
more clearly, but to check them. (Numerical calculations can converge to a grid-
dependent limit, and artifacts of a solution can be numerical rather than geolog-
ical.) Numerical modelling provides a quantitative description and synthesis of a
basin-wide flow in far greater detail than would be feasible analytically. The com-
bination of the two techniques is a much more powerful research tool than either
alone.” Keeping this in mind, we have used the proposed consistent point-searching
interpolation algorithm to develop a general interface between the two commercial
computational codes, FIDAP and FLAC. This development enables us to investigate
the integrated behaviour of ore body formation and mineralization in hydrothermal
systems.
The first application example, which is closely associated with the coupled prob-
lem between medium deformation, pore-fluid flow, heat transfer and reactive mass
transport in a fluid-saturated porous medium, is to answer the question: What is
the pattern of pore-fluid flow, the distributions of temperature, reactant and product