Articles | Volume 8, issue 6
https://doi.org/10.5194/se-8-1181-2017
https://doi.org/10.5194/se-8-1181-2017
Method article
 | 
24 Nov 2017
Method article |  | 24 Nov 2017

Analytical solution for viscous incompressible Stokes flow in a spherical shell

Cedric Thieulot

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Latest update: 22 May 2024
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Short summary
I present a new family of analytical flow solutions to the incompressible Stokes equation in a spherical shell. The velocity is tangential to both inner and outer boundaries, the viscosity is radial, and the solution has been designed so that the expressions for velocity, pressure, and body force are simple to implement in (geodynamics) codes. This forms the basis of a numerical benchmark for convection codes, and I have implemented it in two finite-element codes.