Sequential Methods for Coupled Geomechanics and Multiphase Flow

5.6. NUMERICAL EXAMPLES 155
log ||e ||
10 Pd
log ||e ||
10 ud
0.5
0
−0.5
−1
−1.5
Case 5.1. Convergence analysis
−2
−2.5
FC
FSS (1 iter)
FSN (3 iter)
FSN (2 iter)
FSN (1 iter)
−3
−4.5 −4 −3.5 −3 −2.5 −2 −1.5 −1
log (∆ t )
10 d
−2
−2.5
−3
−3.5
−4
Case 5.1. Convergence analysis
FC
FSS (1 iter)
−4.5
FSN (3 iter)
FSN (2 iter)
FSN (1 iter)
−5
−4 −3.5 −3 −2.5 −2 −1.5 −1
log (∆ t )
10 d
Figure 5.13: Convergence analysis of Case 5.1 on pressure (top) and displacement (bottom).
∆td = 4cv∆t/Lz 2 . FC, FSS, and FSN indicate the fully coupled, fixed-stress, and fixedstrain
split methods, respectively. The fixed-strain split shows zeroth-order accuracy. But,
the fixed-stress split yields first-order accuracy.