Articles | Volume 8, issue 6
Solid Earth, 8, 1181–1191, 2017
https://doi.org/10.5194/se-8-1181-2017
Solid Earth, 8, 1181–1191, 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 Cedric Thieulot
  • Department of Earth Sciences, Utrecht University, Utrecht, the Netherlands

Abstract. 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 of the power-law type, and the solution has been designed so that the expressions for velocity, pressure, and body force are simple polynomials and therefore simple to implement in (geodynamics) codes. Various flow average values, e.g., the root mean square velocity, are analytically computed. This forms the basis of a numerical benchmark for convection codes and I have implemented it in two finite-element codes: ASPECT and ELEFANT. I report error convergence rates for velocity and pressure.

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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.