Page 165 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

7.1 An Equivalent Source Algorithm for Simulating Thermal and Chemical Effects 155

of the Earth, a numerical method needs to be developed to simulate the chemical
consequences of the magma solidification in porous rocks.
A large amount of geochemical research has indicated that intruded magma
in the Earth’s crust has different chemical compositions and, therefore, different
types of rocks can be formed during the solidification and crystallization of the
intruded magma. Both temperature and pressure conditions during solidification of
the magma can also affect the resulting rock types dramatically. Rhyolite and basalt,
instead of granite and gabbro, are formed if the solidification conditions of the fel-
sic and mafic magmas are changed from intrusive into extrusive. It is well known
that the solidus of the intruded magma is mainly dependent on the magma composi-
tion, the contents of water and other volatile fluids. For a particular kind of intruded
magma, the abovementioned information is obtainable from geochemical and iso-
topic analyses. Therefore, given a particular kind of intruded magma, it is possible
to determine the contents of water and other volatile fluids, which should be released
when the intruded magma becomes solidified. This implies that the volatile fluids
released from the intruded magma can be quantitatively simulated in the numerical
analysis, which is another important issue to be addressed in this study.
Due to the complex nature of the magma intrusion problem within the crust
of the Earth, it is useful to conduct numerical simulation of this kind of problem
progressively from a simplistic stage into more complicated stages. This research
methodology is rational because of the multiple time and length scales of the prob-
lem itself. Thus, we plan to solve the magma intrusion problem using the following
three level models. For the first level model, we primarily consider the effects of
the post-solidification magma on pore-fluid flow, heat transfer and ore forming pat-
terns within the upper crust of the Earth. For the second level model, we consider
the thermal and chemical effects of the post-intrusion but pre-solidification magma
on pore-fluid flow, heat transfer and ore forming patterns within the upper crust
of the Earth. In this model, we must develop some useful and efficient computer
algorithms to simulate the magma solidification problem. For the third level model,
we will consider the intrusion process itself at a much smaller scale using parti-
cle mechanics-based computer algorithms. Once efficient numerical algorithms for
dealing with above three level models are developed, it is possible to integrate them
to simulate the whole process of the magma intrusion problem. So far, we have
completed some work for the first level model (Zhao et al. 2003e). In this study, we
will develop some useful and efficient computer algorithms to simulate the magma
solidification problem associated with the second level model.

7.1 An Equivalent Source Algorithm for Simulating
Thermal and Chemical Effects of Intruded Magma
Solidification Problems

Owing to the importance for many scientific issues and technical applications, theo-
retical and numerical analyses of heat transfer with phase change have been carried
out for more than half a century. There is an extensive literature which reports and