Page 45 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

2.6 Application of the Progressive Asymptotic Approach Procedure 31

◦
◦
the top and the bottom of the computational domain are 0 C and 250 C respectively.
Both the top and the bottom of the computational domain are impermeable in the
vertical direction, while all the four side boundaries of the computational domain
are assumed to be insulated and impermeable in the horizontal direction.
Figures 2.13 and 2.14 show the numerical and analytical solutions for the dis-
tributions of pore-fluid velocity and temperature in the axisymmetrical case (i.e.
case 1) respectively. As expected, the numerical solutions for both pore-fluid veloc-
ity and temperature in this case are exactly axisymmetrical about the y axis. This
implies that the three-dimensional problem considered in this particular case can be
reasonably treated as a two-dimensional one. It is also observed that the numerical
solutions in Fig. 2.13 compare very well with the previous solutions in Fig. 2.14

Fig. 2.13 Distributions of pore-fluid velocity and temperature in the porous medium (Case 1,
numerical solutions)