Page 177 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

7.3 Verification and Application of the Equivalent Source Algorithm 167

o
1000 Δ T ( C )
o t=21.73 days
+ t=108.6 days
* t=217.2 days
800
x t=434.4 days
600

400

200

0
0 8.4 16.8 25.2 33.6 42.0
x (m)
(Numerical solution, three-step solidification)

1000 Δ T ( C )
o
o t=21.73 days
+ t=108.6 days
800 * t=217.2 days
x t=434.4 days
600

400

200

0
0 8.4 16.8 25.2 33.6 42.0
x (m)
(Analytical solution)
Fig. 7.5 Comparison of analytical solutions with numerical solutions (Three-step solidification)

elements to simulate the intruded magma in the solidification direction) produce
similar numerical results. This indicates that, due to the precise consideration of the
magma solidification interface, the present numerical algorithm is not sensitive to
the mesh density in the solidification direction of the magma solidification region.
It is noted that, for intruded magma dikes and sills of large aspect ratios, one
could have expected on dimensional considerations that the solidification of the
intruded magma could be treated by means of a one-dimensional model in the solid-
ification direction and that such an approximation is asymptotically valid to the
leading order in the aspect ratio of the dike and sill. Such a one-dimensional (1D)
solidification model could be interactively used with two-dimensional (2D) models
for simulating the thermal field in the surrounding rocks. The use of the resulting