Geoscientific Model Development
Geoscientific Model Development
GMD
Articles | Volume 18, issue 2
Articles | Volume 18, issue 2
https://doi.org/10.5194/gmd-18-563-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
Special issue:
https://doi.org/10.5194/gmd-18-563-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
Articles | Volume 18, issue 2
Development and technical paper
 | 
31 Jan 2025
Development and technical paper |  | 31 Jan 2025

Accelerated pseudo-transient method for elastic, viscoelastic, and coupled hydromechanical problems with applications

Yury Alkhimenkov and Yury Y. Podladchikov

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Cited articles

Alkhimenkov, Y.: Numerical validation of Gassmann’s equations, Geophysics, 88, A25–A29, 2023. a
Alkhimenkov, Y. and Podladchikov, Y.: APTsolver, Zenodo [code and data set], https://doi.org/10.5281/zenodo.14056939, 2024. a
Alkhimenkov, Y., Khakimova, L., and Podladchikov, Y.: Stability of discrete schemes of Biot’s poroelastic equations, Geophys. J. Int., 225, 354–377, 2021a. a, b, c, d, e, f
Alkhimenkov, Y., Räss, L., Khakimova, L., Quintal, B., and Podladchikov, Y.: Resolving wave propagation in anisotropic poroelastic media using graphical processing units (GPUs), J. Geophys. Res.-Sol. Ea., 126, e2020JB021175, https://doi.org/10.1029/2020JB021175, 2021b. a, b, c
Alkhimenkov, Y., Khakimova, L., and Podladchikov, Y.: Shear bands triggered by solitary porosity waves in deforming fluid-saturated porous media, Geophys. Res. Lett., 51, e2024GL108789, https://doi.org/10.1029/2024GL108789, 2024a. a, b
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The accelerated pseudo-transient (APT) method is an efficient way to solve partial differential equations, particularly well-suited for parallel computing. This paper explores the APT method's effectiveness in solving elastic, viscoelastic, and hydromechanical problems, focusing on quasi-static conditions in 1D, 2D, and 3D. The study examines the best numerical settings for fast and accurate solutions. The paper shows how the APT method can handle complex problems in high-resolution models.
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Advances in numerical modelling of geological processes