NUMERICAL-SOLUTION FOR THE DILATION OF A FLUID-SATURATED POROUS ELASTIC SPHERE DUE TO A POINT-SOURCE OF FLUID AT THE CENTER OF THE SPHERE

Mathematical modelling of the ascent of free fluid through relatively strong rock, deep in the Earth's mantle, presents a challenge in geome chanics. Here the medium is considered as fluid-saturated, porous, ela stic and bounded, and the fluid enters at a point source. An explicit finite difference method is developed for the numerical solution to th e problem of the dilatation of a fluid-saturated porous elastic sphere due to a point fluid source of constant strength at the centre of the sphere. A cubic spline interpolant is used to evaluate a definite int egral which occurs in the boundary condition for the pore fluid pressu re at the surface of the sphere. The numerical solutions for the dilat ation and pore fluid pressure are compared with analytical solutions a nd the absolute and relative errors of the numerical solutions are cal culated. When the fluid source is switched on, the pore fluid pressure starts to decrease, reaches a minimum value and then steadily increas es. The initial time rate of decrease of the pore fluid pressure is in dependent of the radial distance from the source. It decreases as the radius of the sphere increases and vanishes for a point fluid source i n an infinite porous elastic medium.