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

Yoon, Hyun C.; Kim, Jihoon

doi:10.1002/nag.3283

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

Journal Article · Tue Oct 19 00:00:00 EDT 2021 · International Journal for Numerical and Analytical Methods in Geomechanics

DOI:https://doi.org/10.1002/nag.3283· OSTI ID:1846000

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Texas A & M Univ., College Station, TX (United States); Korea Institute of Geoscience and Mineral Resources (KIGAM), Daejeon (Korea, Republic of); Texas A&M University
Texas A & M Univ., College Station, TX (United States)

In this work, 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, i.e., 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.

View Accepted Manuscript (DOE)

Research Organization:: Texas A & M Univ., College Station, TX (United States). Texas A & M Engineering Experiment Station

Sponsoring Organization:: USDOE Office of Fossil Energy (FE); Korea Institute of Geoscience and Mineral Resources (KIGAM)

Grant/Contract Number:: FE0028973

OSTI ID:: 1846000

Report Number(s):: DOE-TAMU--FE0028973-17

Journal Information:: International Journal for Numerical and Analytical Methods in Geomechanics, Journal Name: International Journal for Numerical and Analytical Methods in Geomechanics Journal Issue: 18 Vol. 45; ISSN 0363-9061

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

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