Page 174 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

164 7 Simulating Thermal and Chemical Effects of Intruded Magma Solidification Problems

a physical equivalent problem which can be solved using the conventional fixed-
mesh finite element method, it is necessary to use a benchmark magma solidifica-
tion problem, for which the analytical solution is available, to verify the proposed
algorithm. As mentioned in the previous section, the effect of the released volatile
fluids on the heat transfer and magma solidification is negligible due to the rela-
tively small amount of their volumetric mass sources. On the other hand, transport
of the released volatile fluids can be treated as a conventional mass transport prob-
lem, for which the conventional finite element method has been used for many years
(Zienkiewicz 1977). This indicates that we only need to verify the proposed algo-
rithm for simulating the heat transfer process associated with the intruded magma
solidification. For the above reasons, only the heat transfer process associated with
the benchmark magma solidification problem is considered to verify the proposed
algorithm. Figure 7.3 shows the finite element mesh of the benchmark magma solid-
ification problem. In this figure, the original magma intruded region, which is indi-
cated in black in the finite element mesh of the whole computational domain, is

(Finite element mesh of the whole computational domain)

y

0 x
(Detailed mesh for the intruded magma solidification domain)
Fig. 7.3 Finite element mesh of the benchmark magma solidification problem