Page 176 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

166 7 Simulating Thermal and Chemical Effects of Intruded Magma Solidification Problems

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, one-step solidification)
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)
(Analytical solution)

Fig. 7.4 Comparison of analytical solutions with numerical solutions (One-step solidification)
the proposed equivalent algorithm for simulating solidification effects of magma
intrusion problems in porous rocks can produce highly accurate numerical solu-
tions. Since the numerical solution from the one-step solidification model has sim-
ilar accuracy to that from the three-step solidification model, the one-step solidifi-
cation model is useful for simulating thermal effects of dike-like magma intrusion
problems in porous rocks. For the purpose of examining the numerical solution sen-
sitivity to the mesh density in the magma solidification direction, we have doubled
and tripled the mesh density in the magma solidification region. Since the solidi-
fication interface between the rock and intruded magma is precisely considered in
the magma solidification direction, all the three meshes of the original mesh density
(i.e. 240 finite elements to simulate the intruded magma in the solidification direc-
tion), the doubled mesh density (i.e. 480 finite elements to simulate the intruded
magma in the solidification direction) and the tripled mesh density (i.e. 720 finite