An efficient staggered time-marching procedure for porodynamics

Abstract

The present work proposes a novel time-marching procedure, which is designed for the dynamic simulation of the coupled two phase Biot equations, considering the displacement–pressure (u−p) formulation. The new approach provides unconditional stability and excellent efficiency. Due to the staggered character of the temporal discretization, where equilibrium is established at time t for the u group of governing equations and at time t+Δt for the p group of governing equations, the resulting systems of equations have an improved format and can be factorized/solved at significantly less computational effort when compared to standard approaches, such as the generalized Newmark scheme. In addition, the resulting new systems of equations are characterized by considerably lower condition numbers, reducing correlated numerical issues. Unconditional stability is achieved by a consistent manipulation of the mass and compressibility matrix of the model, which causes virtually no computational overhead. As a byproduct of the altered compressibility matrix, the method is capable of simulating incompressible and impermeable phenomena without the need for any further feats. The newly developed time-marching technique is implemented and tested considering different benchmark problems. For comparison, the commonly used Newmark scheme is also applied and both direct (LU decomposition) and iterative (GMRES) linear solvers are employed, in order to assess the efficiency of the new technique.