Geoscientific Model Development
Geoscientific Model Development
GMD
Articles | Volume 19, issue 18
Articles | Volume 19, issue 18
https://doi.org/10.5194/gmd-19-8839-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
Special issue:
https://doi.org/10.5194/gmd-19-8839-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
Articles | Volume 19, issue 18
Development and technical paper
 | 
21 Sep 2026
Development and technical paper |  | 21 Sep 2026

Variational Stokes method applied to free surface boundaries in numerical geodynamical models using the staggered-grid finite-difference discretisation

Timothy S. Gray, Paul J. Tackley, and Taras V. Gerya

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Latest update: 21 Sep 2026
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Short summary
We developed a new way to model how planetary surfaces rise and sink as the deep interior slowly flows. Existing approaches are either costly or unstable. Our method represents the surface smoothly within a fixed grid, which avoids artificial air layers and numerical problems. Tests show it matches established results while running faster and working in more realistic settings, such as loaded surfaces and global models. This makes simulations of surface evolution more reliable and accessible.
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Special issue
Advances in numerical modelling of geological processes