Journal of Conference Abstracts

A Local Mesh Refinement Multigrid Method for 3D Mantle Convection with Strongly Temperature-dependent Viscosity

Michael Albers (mab@geo.physik.uni-goettingen.de)

Institut fuer Geophysik, Herzberger Landstr. 180, Goettingen, 37075, Germany

Convection in the Earth or other planetary mantles is strongly dominated by the temperature-dependence of viscosity which is often neglected in 3D convection models because of limited computer resources. Therefore, the development of efficient numerical methods is important for geodynamic modeling.

I have developed a multigrid method for solving the Boussinesq-equations in Cartesian geometry with primitive variables on a staggered grid that remains stable for viscosity contrasts up to 10⁸ without significant increase of computational effort. Multigrid iterations have the advantage over other iterative methods that their computational effort increases only linearly with the number of grid points. This makes multigrid methods very efficient in solving differential equations when grids with large number of grid points are used.

Interesting features for investigations in mantle convection models are for example narrow plumes or plate boundaries. These regions require a grid with small grid spacing to obtain a well-resolved solution. I present a simple and highly flexible technique of implementing local mesh refinements in multigrid methods. The non-uniform grid is generated by a set of uniform subgrids which cover only parts of the model domain. The differential equations are only solved on these uniform subgrids. Important for the accuracy of this method is the order of interpolation used to calculate the boundary values of the subgrids for which a cubic interpolation is necessary. This mesh refinement technique offers the possibility of adaptive grid refinements.

The numerical method is applied to investigations of plume-lithosphere-interaction near mid-ocean ridges.