Articles | Volume 5, issue 1
Solid Earth, 5, 461–476, 2014
https://doi.org/10.5194/se-5-461-2014
Solid Earth, 5, 461–476, 2014
https://doi.org/10.5194/se-5-461-2014

Research article 10 Jun 2014

Research article | 10 Jun 2014

Practical analytical solutions for benchmarking of 2-D and 3-D geodynamic Stokes problems with variable viscosity

I. Yu. Popov2, I. S. Lobanov2, S. I. Popov2, A. I. Popov2, and T. V. Gerya1 I. Yu. Popov et al.
  • 1Institute of Geophysics, Department of Earth Sciences, Swiss Federal Institute of Technology Zurich (ETH), 5 Sonnegstrasse, 8092 Zurich, Switzerland
  • 2St. Petersburg National Research University of Information Technologies, Mechanics and Optics, 49 Kronverkskiy, St. Petersburg, 197101, Russia

Abstract. Geodynamic modeling is often related with challenging computations involving solution of the Stokes and continuity equations under the condition of highly variable viscosity. Based on a new analytical approach we have developed particular analytical solutions for 2-D and 3-D incompressible Stokes flows with both linearly and exponentially variable viscosity. We demonstrate how these particular solutions can be converted into 2-D and 3-D test problems suitable for benchmarking numerical codes aimed at modeling various mantle convection and lithospheric dynamics problems. The Main advantage of this new generalized approach is that a large variety of benchmark solutions can be generated, including relatively complex cases with open model boundaries, non-vertical gravity and variable gradients of the viscosity and density fields, which are not parallel to the Cartesian axes. Examples of respective 2-D and 3-D MatLab codes are provided with this paper.

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