Page 48 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

34 2 Simulating Steady-State Natural Convective Problems

(t = 0s) (t = 1 × 10 13 s)

13
(t = 2 × 10 13 s) (t = 3 × 10 s)

13
(t = 4 × 10 13 s) (t = 5 × 10 s)
Fig. 2.16 Particle trajectories in the porous medium (Case 1)

We selected 24 particles, 12 of which are in the front plane and the rest are
in the back plane of the computation domain, to view the trajectories of those
particles. Figure 2.16 shows the particle trajectories in the porous media for several
different time instants in case 1. It is clear that in this case, all the particles move
within the planes they are initially located within (at t = 0s), because the convective
pore-fluid flow (in case 1) is essentially axisymmetrical about the rotation axis of
these particles considered. Figures 2.17 and 2.18 show the particle trajectories in
the porous media for several different time instants in case 2. It is observed that the
particle trajectories shown in case 2 are totally different from those shown in case
1, although the initial locations (at t = 0s) of these 24 particles are exactly the same
for these two cases. In fact, the particle trajectories shown in case 2 are much more
complicated than those shown in case 1. Since pore-fluid is often the sole agent to
carry the minerals from the lower crust to the upper crust of the Earth, the differ-
ent patterns of particle trajectories imply that the pattern of ore body formation and
mineralization may be totally different in those two three-dimensional hydrothermal
systems.