Fluidity: A fully unstructured anisotropic adaptive mesh computational modeling framework for geodynamics

We present a new computational modeling framework, Fluidity, for application to a range of two- and three-dimensional geodynamic problems, with the focus here on mantle convection. The approach centers upon a finite element discretization on unstructured simplex meshes, which represent complex geometries in a straightforward manner. Throughout a simulation, the mesh is dynamically adapted to optimize the representation of evolving solution structures. The adaptive algorithm makes use of anisotropic measures of solution complexity, to vary resolution and allow long, thin elements to align with features such as boundary layers. The modeling framework presented differs from the majority of current mantle convection codes, which are typically based upon fixed structured grids. This necessitates a thorough and detailed validation, which is a focus of this paper. Benchmark comparisons are undertaken with a range of two- and three-dimensional, isoviscous and variable viscosity cases. In addition, model predictions are compared to experimental results. Such comparisons highlight not only the robustness and accuracy of Fluidity but also the advantages of anisotropic adaptive unstructured meshes, significantly reducing computational requirements when compared to a fixed mesh simulation.