Using an iterative field-split solver for the quasistatic Biot equation
https://doi.org/10.18303/2619-1563-2024-1-19
Abstract
Quasistatic Biot equations in the frequency domain are applied to model low-frequency loading of the fractured porous rock sample. We approximate Biot equations by a finite-difference scheme on the staggered grid, defining different field components at different grid points. To solve the resulting system of linear algebraic equations (SLAE) with more than 106 unknown values, we use an iterative method (Biconjugate gradient stabilized method, BCGStab) with a preconditioner based on field-split approach to divide equations into two groups. The first group describes solid deformation, and the second group describes fluid transport. Numerical experiments demonstrate fast convergence of the iterative process for applied method and its advantages in the case of large computational grid in comparison with direct method.
Keywords
poroelasticity,
Biot equation,
finite differences,
direct methods for SLAE,
iterative methods,
field-split preconditioner
Supporting agencies: The study was carried out as part of government assignment to the Russian Academy of Sciences in basic research, Project FWZZ-2022-0022, and supported by the Russian Science Foundation, Project No. 19-77-20004-P.
About the Authors
S. А. Solovyev
Sobolev Institute of Mathematics SB RAS
Russian Federation
Russian Federation
4, Koptyug Ave., Novosibirsk, 630090.
V. I. Kostin
Trofimuk Institute of Petroleum Geology and Geophysics, SB RAS
Russian Federation
Russian Federation
3, Koptyug Ave., Novosibirsk, 630090.
V. V. Lisitsa
Trofimuk Institute of Petroleum Geology and Geophysics, SB RAS
Russian Federation
Russian Federation
3, Koptyug Ave., Novosibirsk, 630090.
M. A. Novikov
Sobolev Institute of Mathematics SB RAS
Russian Federation
Russian Federation
4, Koptyug Ave., Novosibirsk, 630090.
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Review
For citations:
Solovyev S.А., Kostin V.I., Lisitsa V.V., Novikov M.A. Using an iterative field-split solver for the quasistatic Biot equation. Russian Journal of Geophysical Technologies. 2024;(1):19-28. (In Russ.) https://doi.org/10.18303/2619-1563-2024-1-19
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