VON-NEUMANN STABILITY ANALYSIS OF BIOT GENERAL 2-DIMENSIONAL THEORY OF CONSOLIDATION

Von Neumann stability analysis is performed for a Galerkin finite elem ent formulation of Blot's consolidation equations on two-dimensional b ilinear elements. Two dimensionless groups-the Time Factor and Void Fa ctor-are identified and these quantities, along with the time-integrat ion weighting, are used to explore the stability implications for vari ations in physical property and discretization parameters. The results show that the presence and persistence of stable spurious oscillation s in the pore pressure are influenced by the ratio of time-step size t o the square of the space-step for fixed time-integration weightings a nd physical property selections. In general, increasing the time-step or decreasing the mesh spacing has a smoothing effect on the discrete solution, however, special cases exist that violate this generality wh ich can be readily identified through the Von Neumann approach. The an alysis also reveals that explicitly dominated schemes are not stable f or saturated media and only become possible through a decoupling of th e equilibrium and continuity equations. In the case of unsaturated med ia, a break down in the Von Neumann results has been shown to occur du e to the influence of boundary conditions on stability. (C) 1998 John Wiley & Sons, Ltd.