Sequential Methods for Coupled Geomechanics and Multiphase Flow

4.4. NUMERICAL EXAMPLES 107
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 4.10: Convergence analysis of pressure (top) and displacement (bottom) for an
incompressible fluid, where τ = 9.5 × 10 11 ∼ = ∞ and cf = 3.5 × 10 −20 Pa −1 ∼ = 0. The
undrained split is not convergent, showing zeroth-order accuracy. But, the fully coupled
method shows first-order accuracy.