Solar cycle modelling using spatiotemporal decomposition schemes

We introduce a novel technique for the numerical solution of systems of advection–diffusion partial differential equations with non-linear source terms. The method is based on a spatiotemporal decomposition that makes use of any conventional spatial and temporal discretization schemes, and is applicable to either explicit or implicit time-integration. In the case of spatially localized source terms, the decomposition allows severe truncation of the resulting algebraic system. The technique and its variations are introduced in the context of the magnetohydrodynamical dynamo equations describing the evolution of the large-scale magnetic field of the sun and stars, but they are of more general applicability. We offer a few examples showing the usefulness of this technique in the solar dynamo context, not only for the computation of numerical solutions per se, but also as an analysis tool to better understand the behavior of the solutions on long temporal scales.