Sequential Methods for Coupled Geomechanics and Multiphase Flow

4.4. NUMERICAL EXAMPLES 105
log ||e ||
10 Pd
log ||e ||
10 ud
0.5
0
−0.5
−1
−1.5
−2
−2.5
−3
−3.5
−4
−4.5
−1.5
−2
−2.5
−3
−3.5
−4
−4.5
−5
−5.5
−6
Convergence analysis of pressure
FC
Und (1 iter)
−4 −3 −2
log (∆ t )
10 d
−1 0
Convergence analysis of displacement
FC
Und (1 iter)
−4 −3 −2
log (∆ t )
10 d
−1 0
Figure 4.8: Convergence analysis of pressure (top) and displacement (bottom) for a nearly
incompressible fluid, where τ = 9.5 ×10 4 and cf = 3.5 ×10 −13 Pa −1 . The staggered method
is used. The undrained split is not convergent, showing almost zeroth-order accuracy. The
fully coupled method shows first-order accuracy.