Computational Modeling of Volcanism on Earth-like Planets

The aim of this paper is to model the level of volcanic activity on Earth-like planets over time. We consider the level of volcanic activity on a planet to be a function of the planetu0027s thermodynamic state. A planet is considered to become volcanically inactive once it has reached a thermodynamic steady state. We first model the heat flow in the planetu0027s interior by the heat equation, which we reduce to a one-dimensional Laplace equation. We then calculate the temperature field of the planet by numerically solving a spherically symmetric boundary value problem. Finally, we relate discrete time-steps in our simulation to real-time via an empirically- informed mapping. Our results indicate that Earth will remain volcanically active for a total of billion years