Numerical studies of thermal convection with temperature-and pressure-dependent viscosity at extreme viscosity contrasts

Motivated by convection of planetary mantles, we consider a mathematical model for Rayleigh-Benard convection in a basally heated layer of a fluid whose viscosity depends strongly on temperature and pressure, defined in an Arrhenius form. The model is solved numerically for extremely large viscosity variations across a unit aspect ratio cell, and steady solutions for temperature, isotherms, and streamlines are obtained. To improve the efficiency of numerical computation, we introduce a modified viscosity law with a low temperature cutoff. We demonstrate that this simplification results in markedly improved numerical convergence without compromising accuracy. Continued numerical experiments suggest that narrow cells are preferred at extreme viscosity contrasts, and this conclusion is supported by a linear stability analysis. (C) 2015 AIP Publishing LLC.