Sequential Methods for Coupled Geomechanics and Multiphase Flow

4.4. NUMERICAL EXAMPLES 99
Figure 4.3: Case 4.1: the Terzaghi problem in one dimension (left). Case 4.2: the consolidation
problem in two dimensions (right).
decrease as O(∆t). This confirms that the undrained and fully coupled methods have O(∆t)
accuracy in time. However, the drained split does not show convergence. In particular, one
iteration of the drained split yields zeroth-order accuracy, which supports the a-priori error
estimate. Figures 4.5 and 4.6 show the spatial distributions of pressure and displacement by
the drained and undrained splits, respectively. As the time step size is refined, the drained
split with one iteration does not converge to the true solution, but to a different solution,
even though the distributions of pressure and displacement look plausible. On the other
hand, the undrained spit with one iteration converges to the true solution. When even
iteration numbers are used, the drained split shows better convergence in time, whereas
odd iteration numbers show less accurate solutions.
Figure 4.7 shows a comparison between taking more iterations for a fixed time step
and refining the time step size under the same computational cost for the drained split.
Performing more iterations is a better strategy for the drained split than refining the time