Page 47 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

2.6 Application of the Progressive Asymptotic Approach Procedure 33

Fig. 2.15 Distributions of pore-fluid velocity and temperature in the porous medium (Case 2)

Figure 2.15 shows the numerical solutions for the distributions of pore-fluid
velocity and temperature in the real three-dimensional case (i.e. case 2). By com-
paring the numerical solutions from case 1 (Fig. 2.13) with those from case 2
(Fig. 2.15), it is observed that the distribution patterns of both pore-fluid velocity
and temperature are totally different for these two cases. This demonstrates that the
perturbation of gravity at different planes may have a significant effect on the pat-
tern of convective pore-fluid flow in three-dimensional hydrothermal systems. Just
like two-dimensional convective flow problems, the solution dependence of three-
dimensional convective flow on the direction of the perturbation of gravity need to
be considered when these kinds of results are interpreted.
To further observe the movements of pore-fluid particles, the particle tracking
technique introduced in this section is used during the numerical computation.