Sequential Methods for Coupled Geomechanics and Multiphase Flow

156 CHAPTER 5. FIXED-STRAIN AND FIXED-STRESS SPLITS
Dimensionless distance (z/Lz)
Dimensionless distance (z/Lz)
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
The fixed−strain split (1 iteration, ∆ t d =4c v ∆ t/Lz 2 )
∆ t d =2.6×10 −2
∆ t d =1.04×10 −2
∆ t d =5.2×10 −3
∆ t d =5.2×10 −4
∆ t d =2.6×10 −4
∆ t d =1.04×10 −4
∆ t d =5.2×10 −5
True solution
0
0 0.5 1 1.5
Dimensionless pressure P =(P−P )/∆p
d i i
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
The fixed strain split (1 iteration, ∆ t d =4c v ∆ t/Lz 2 )
∆ t d =2.6×10 −2
∆ t d =1.04×10 −2
∆ t d =5.2×10 −3
∆ t d =5.2×10 −4
∆ t d =2.6×10 −4
∆ t d =1.04×10 −4
∆ t d =5.2×10 −5
True solution
0
0 0.005 0.01 0.015 0.02 0.025 0.03
Dimensionless displacement u =u/L
d z
Figure 5.14: Non-convergence of the fixed-strain split with one iteration for Case 5.1: pressure
(top) and displacement (bottom)