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Hybrid Fixed-Point Fixed-Stress Splitting Method for Linear Poroelasticity

1
Department of Computational Science, University of Texas, El Paso, TX 79968, USA
2
Department of Mechanical Engineering, University of Texas, El Paso, TX 79968, USA
*
Author to whom correspondence should be addressed.
Geosciences 2019, 9(1), 29; https://doi.org/10.3390/geosciences9010029
Received: 8 November 2018 / Revised: 28 December 2018 / Accepted: 2 January 2019 / Published: 8 January 2019
(This article belongs to the Special Issue Advances in Computational Geomechanics)
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Abstract

Efficient and accurate poroelasticity models are critical in modeling geophysical problems such as oil exploration, gas-hydrate detection, and hydrogeology. We propose an efficient operator splitting method for Biot’s model of linear poroelasticity based on fixed-point iteration and constrained stress. In this method, we eliminate the constraint on time step via combining our fixed-point approach with a physics-based restraint between iterations. Three different cases are considered to demonstrate the stability and consistency of the method for constant and variable parameters. The results are validated against the results from the fully coupled approach. In case I, a single iteration is used for continuous coefficients. The relative error decreases with an increase in time. In case II, material coefficients are assumed to be linear. In the single iteration approach, the relative error grows significantly to 40% before rapidly decaying to zero. This is an artifact of the approximate solutions approaching the asymptotic solution. The error in the multiple iterations oscillates within 10 6 before decaying to the asymptotic solution. Nine iterations per time step are enough to achieve the relative error close to 10 7 . In the last case, the hybrid method with multiple iterations requires approximately 16 iterations to make the relative error 5 × 10 6 . View Full-Text
Keywords: numerical method; hybrid method; poroelasticity; geomechanics; multiphase numerical method; hybrid method; poroelasticity; geomechanics; multiphase
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Delgado, P.M.; Kotteda, V.M.K.; Kumar, V. Hybrid Fixed-Point Fixed-Stress Splitting Method for Linear Poroelasticity. Geosciences 2019, 9, 29.

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