Daspk: A New High Order And Adaptive Time-Integration Technique With Applications To Mantle Convection With Strongly Temperature-And Pressure-Dependent Rheology

A new technique is presented for the efficient time-integration of the equations that describe the slow deformation in the Earth's mantle. This method is based on the adaptive, high order implicit solver for differential-algebraic equations (DASPK) and is independent of the choice of spatial discretization technique. Using a standard finite element package for the spatial discretization, it is shown that the solution of the 2-D convection-diffusion equation for temperature can be performed at much lower computational cost, but at the same or higher accuracy, compared to a traditional implicit second-order method. The solution to the full set of 2-D mantle convection equations is 3 to 4 times more efficient. Both in 2-D and 3-D, the memory and CPU-usage of this implementation depends linearly on the number of grid points and has good properties with respect to vectorization and parallelization. As an application of this technique, convection in the Earth's mantle with strongly temperature and pressure dependent rheology is studied in axisymmetric geometry. Models are developed that are consistent with current estimates of surface heat flow and radial viscosity distribution. General characteristics are: a dynamic upper mantle overlying a near-stationary lower mantle; strong plumes rising from the coremantle boundary, even at high rates of internal heating; and an effective Rayleigh number of nearly two orders of magnitudes lower than commonly used values in the range of 107 to 108.