Page 163 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

Chapter 7
An Equivalent Source Algorithm for Simulating

Thermal and Chemical Effects of Intruded
Magma Solidification Problems

Consideration of the effects of magma ascending and solidification is important to
the further understanding of ore body formation and mineralization in the crust of
the Earth. Although various possible fundamental mechanisms of magma ascending
in the crust are proposed (Johnson and Pollard, 1973, Marsh 1982, Lister and Kerr
1991, Rubin 1995, Weinberg 1996, Bons et al. 2001), the development of numeri-
cal algorithms for simulating the proposed magma ascending mechanisms is still
under-developed. For example, continuum-mechanics-based numerical methods
have encountered serious difficulties in simulating the random generation and prop-
agation of hydro-fractured cracks, the magma flow within these cracks, the solidifi-
cation of the ascending magma due to heat losses to the surrounding rocks, and so
forth. In order to overcome these difficulties, particle-based numerical simulations
have been developed rapidly in recent years (Zhao et al. 2006f, 2007b, c, d, 2008g).
However, due to the different time and length scales involved in ore body formation
and mineralization problems, it is also very difficult, even if not impossible, to use
the present particle-based numerical methods to simulate all the important processes
associated with ore body formation and mineralization problems in the crust of the
Earth. As a long-term development strategy, we need to develop multiple time and
length scale modelling techniques and algorithms so that particle simulation meth-
ods, combined with newly-developed techniques and algorithms, can be used to
solve such large scale geological problems. As an expedient strategy, although it is
impossible to use the continuum-mechanics-based numerical methods to simulate
directly the magma ascent processes, we can develop some useful algorithms, in
combination with continuum-mechanics-based numerical methods, to simulate the
effects of the magma ascent processes. Thus, the main motivation of carrying out
this study is to develop a useful algorithm to consider the dynamic consequences
involved in magma ascent processes using continuum-mechanics-based numerical
methods.
In terms of the magma intrusion mechanism, a large amount of theoretical work
has been carried out previously, even though it is based on simple conceptual mod-
els (Johnson and Pollard, 1973, Marsh 1982, Lister and Kerr 1991, Rubin 1995,
Weinberg 1996, Bons et al. 2001). Although the previous theoretical work needs to
be quantitatively refined, it can be used to estimate the total volume of the intruded

C. Zhao et al., Fundamentals of Computational Geoscience, 153
Lecture Notes in Earth Sciences 122, DOI 10.1007/978-3-540-89743-9 7,
C Springer-Verlag Berlin Heidelberg 2009