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

Model code and software

ASPECT: Advanced Solver for Problems in Earth’s ConvecTion, User Manual W. Bangerth, J. Dannberg, R. Gassmöller, T. Heister, and others https://doi.org/10.6084/m9.figshare.4865333

Download
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.