Articles | Volume 8, issue 6
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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Cited articles

Arrial, P.-A., Flyer, N., Wright, G. B., and Kellogg, L. H.: On the sensitivity of 3-D thermal convection codes to numerical discretization: a model intercomparison, Geosci. Model Dev., 7, 2065–2076,, 2014.
Bangerth, W., Hartmann, R., and Kanschat, G.: deal.II – a general purpose object oriented finite element library, ACM T. Math. Software, 33,, 2007.
Bangerth, W., Davydov, D., Heister, T., Heltai, L., Kanschat, G., Kronbichler, M., Maier, M., Turcksin, B., and Wells, D.: The deal.ii library, version 8.4, J. Numer. Math., 24,, 2016.
Bangerth, W., Dannberg, J., Gassmöller, R., Heister, T., and others: ASPECT: Advanced Solver for Problems in Earth's ConvecTion, User Manual,, 2017.
Bercovici, D., Schubert, G., Glatzmaier, G., and Zebib, A.: Three-dimensional thermal convection in a spherical shell, J. Fluid Mech., 206, 75–104, 1989.
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.