Page 39 - Fundamentals of Computational Geoscience Numerical Methods and Algorithms

2.6 Application of the Progressive Asymptotic Approach Procedure 25

Fig. 2.9 Dimensionless velocity distribution for different basins

due to different basin shapes for Ra = 80 and Ra = 400 respectively. It is obvi-
ous that different basin shapes have a considerable effect on the patterns of con-
vective flow in the fluid-saturated porous medium, especially in the case of higher
Rayleigh numbers. Apart from notable differences in velocity distribution patterns,
maximum velocity amplitudes for three different basins are also significantly differ-
ent. For instance, in the case of Ra = 80, the maximum amplitudes of dimensionless
velocities are 5.29, 8.93 and 11.66 for square, rectangular and trapezoidal basins
respectively. This fact indicates that different basin shapes may affect the contami-
nant transport or mineralization processes in a fluid-saturated porous medium once
natural convection is initiated in the medium.