Imperial College London
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Stephan Kramer

Faculty of Engineering, Department of Earth Science & Engineering

Advanced Research Fellow
 
 
 
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Contact

 

s.kramer Website CV

 
 
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Location

 

4.85Royal School of MinesSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Kramer:2021:10.5194/gmd-14-1899-2021,
author = {Kramer, S and Davies, R and Wilson, C},
doi = {10.5194/gmd-14-1899-2021},
journal = {Geoscientific Model Development},
pages = {1899--1919},
title = {Analytical solutions for mantle flow in cylindrical and spherical shells},
url = {http://dx.doi.org/10.5194/gmd-14-1899-2021},
volume = {14},
year = {2021}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - Computational models of mantle convection must accurately represent curved boundaries and the associated boundary conditions of a 3-D spherical shell, bounded by Earth's surface and the core–mantle boundary. This is also true for comparable models in a simplified 2-D cylindrical geometry. It is of fundamental importance that the codes underlying these models are carefully verified prior to their application in a geodynamical context, for which comparisons against analytical solutions are an indispensable tool. However, analytical solutions for the Stokes equations in these geometries, based upon simple source terms that adhere to physically realistic boundary conditions, are often complex and difficult to derive. In this paper, we present the analytical solutions for a smooth polynomial source and a delta-function forcing, in combination with free-slip and zero-slip boundary conditions, for both 2-D cylindrical- and 3-D spherical-shell domains. We study the convergence of the Taylor–Hood (P2–P1) discretisation with respect to these solutions, within the finite element computational modelling framework Fluidity, and discuss an issue of suboptimal convergence in the presence of discontinuities. To facilitate the verification of numerical codes across the wider community, we provide a Python package, Assess, that evaluates the analytical solutions at arbitrary points of the domain.
AU  - Kramer,S
AU  - Davies,R
AU  - Wilson,C
DO  - 10.5194/gmd-14-1899-2021
EP  - 1919
PY  - 2021///
SN  - 1991-959X
SP  - 1899
TI  - Analytical solutions for mantle flow in cylindrical and spherical shells
T2  - Geoscientific Model Development
UR  - http://dx.doi.org/10.5194/gmd-14-1899-2021
UR  - https://gmd.copernicus.org/articles/14/1899/2021/
UR  - http://hdl.handle.net/10044/1/88254
VL  - 14
ER  -
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