FINITE-ELEMENT ANALYSIS OF STEADY-STATE NATURAL-CONVECTION PROBLEMS IN FLUID-SATURATED POROUS-MEDIA HEATED FROM BELOW

In this paper, a progressive asymptotic approach procedure is presente d for solving the steady-state Horton-Rogers-Lapwood problem in a flui d-saturated porous medium. The Horton-Rogers-Lapwood problem possesses a bifurcation and, therefore, makes the direct use of conventional fi nite element methods difficult. Even if the Rayleigh number is high en ough to drive the occurrence of natural convection in a fluid-saturate d porous medium, the conventional methods will often produce a trivial non-convective solution. This difficulty can be overcome using the pr ogressive asymptotic approach procedure associated with the finite ele ment method. The method considers a series of modified Horton-Rogers-L apwood problems in which gravity is assumed to tilt a small angle away from vertical. The main idea behind the progressive asymptotic approa ch procedure is that through solving a sequence of such modified probl ems with decreasing tilt, an accurate non-zero velocity solution to th e Horton-Rogers-Lapwood problem can be obtained. This solution provide s a very good initial prediction for the solution to the original Hort on-Rogers-Lapwood problem so that the non-zero velocity solution can b e successfully obtained when the tilted angle is set to zero. Comparis on of numerical solutions with analytical ones to a benchmark problem of any rectangular geometry has demonstrated the usefulness of the pre sent progressive asymptotic approach procedure. Finally, the procedure has been used to investigate the effect of basin shapes on natural co nvection of pore-fluid in a porous medium. (C) 1997 by John Wiley & So ns, Ltd.