Accurate and stablised time integration strategy for saturated porous media dynamics

When applying equal-order monolithic schemes for the solution of incompressible fluid saturated porous media dynamics, the resulting pressure field often exhibit spurious oscillations. This is in part due to violation of the inf-sup restriction. Although the mixed order monolithic scheme such as Taylor–Hood element scheme can circumvent this problem and yet use a mixed order monolithic scheme, a reduction of accuracy of both displacements and pressures may happen when the porous media permeability is small. In this paper, we present a new equal-order monolithic scheme that can accurately handle a broader range of permeabilities. We consider the u-p and u-v-p formulations from the theory of porous media (u:solid displacement, v:liquid velocity, p:liquid pressure) for fully saturated materials. We name the new scheme as the fractional steps correction method. Results show that this scheme succeeds in solving both formulations quite well with a spatial discretisation based on either the finite difference or the finite element method.