Numerical Modeling of Subduction

The long-term evolution of the Earth's interior can be studied using computational simulations, which provide numerical approximations to a set of partial differential equations describing the conservation of momentum, mass, and energy. Here, we present the governing equations suitable for describing the long-term dynamics of the Earth's rocky interior and discuss a range of numerical methods that are suitable to both discretize and solve the conservation equations. Our presentation of numerical methods is framed around modeling subduction. We discuss the specific physical characteristics of a broad class of different subduction models which present methodological challenges, and discuss state-of-the-art approaches to address them. With the intent of using numerical models of subduction for predictive purposes, special attention is given to issues related to obtaining accurate, stable, and robust numerical solutions.