Sequential Methods for Coupled Geomechanics and Multiphase Flow

6.6. NUMERICAL EXAMPLES WITH THE STAGGERED METHOD 205
difference decreases significantly because the fixed-stress split uses updated information
from the mechanical problem, capturing the effect of the instantaneous loading. After the
second iteration, the fixed-stress shows the same convergence behavior as the fully coupled
method.
6.6 Numerical Examples with the staggered method
We perform numerical simulation with the staggered method, reusing Case 6.2. The top of
Figure 6.8 shows the results from the drained and fixed-strain splits. At early time, the two
splits are stable because the coupling strength is below unity even though they have severe
oscillation. However, the coupling strength increases during simulation because of injection
of the less compressible fluid, namely, water. Then the solutions of the drained and fixed
strain splits become unstable because the coupling strength exceeds unity eventually. On
the other hand, the undrained and fixed-stress splits are stable for all time. The bottom of
Figure 6.8 illustrates that the solutions of the undrained and fixed-stress splits are stable
with good accuracy with one or two iterations.