Hybrid Fixed-Point Fixed-Stress Splitting Method for Linear Poroelasticity
AbstractEfficient 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
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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.
Delgado PM, Kotteda VMK, Kumar V. Hybrid Fixed-Point Fixed-Stress Splitting Method for Linear Poroelasticity. Geosciences. 2019; 9(1):29.Chicago/Turabian Style
Delgado, Paul M.; Kotteda, V. M.K.; Kumar, Vinod. 2019. "Hybrid Fixed-Point Fixed-Stress Splitting Method for Linear Poroelasticity." Geosciences 9, no. 1: 29.
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