Spectral deferred correction methods for high‐order accuracy in poroelastic problems

Abstract

We investigate high‐order accuracy in time integration by examining two operator splitting methods for poroelastic problems: the two‐pass and the spectral deferred correction (SDC) methods. To enhance the order of accuracy, the two‐pass method partitions a coupled operator symmetrically, whereas the SDC method corrects truncation errors by establishing an error equation. These high‐order methods are applied to underlying solution strategies, that is, monolithic, fixed‐stress sequential, and undrained sequential methods. We observe that semi‐discretized systems from spatial discretization have forms similar to those of index‐1 differential algebraic equations (DAEs), causing order reduction against the two‐pass method when it is used in conjunction with either the monolithic or sequential method. On the other hand, the SDC in conjunction with the monolithic method exhibits the desired second‐order accuracy in poroelastic problems while increasing the order of accuracy for index‐1 DAEs. However, the SDC in conjunction with either of the two sequential methods does not achieve the desired order of accuracy, and maintains first order because the flow equation for poroelasticity has an additional approximation associated with the volumetric strain rate term, which does not yield exactly the same forms as those of conventional DAEs. Thus, the monolithic SDC method can achieve higher‐order accuracy, but may require higher computational costs because it involves solving matrix systems larger than those for the sequential methods.

Integration of Electromagnetic Geophysics Forward Simulation in Coupled Flow and Geomechanics for Monitoring a Gas Hydrate Deposit Located in the Ulleung Basin, East Sea, Korea

“…For the elastoplastic regime in the geomechanics, we employ the Mohr-Coulomb failure model for the elastoplasticity regime in the ROCMECH within the small deformation theory and the infinitesimal transformation. By coding the interface formulation using Equation (28), we can then capture the changes in reservoir pressure due to compaction of the reservoirs, such as the Mandel-Cryer effect [28,46]. Note that the heat and geomechanics are loosely coupled with the one-way coupling, for which from heat to geomechanics only is considered.…”