The birth of a volcano: A nonlinear convective model for rock melting at the asthenosphere—Lithosphere boundary

The investigation of the physical processes determining the melting of the lithospheric rocks is of crucial importance for understanding the volcanic dynamics and its related consequences. Rock melting begins when a sufficiently high temperature is experienced by the rock solidus. The heat transfer from the asthenosphere to the lithosphere can be assumed as the main mechanism accountable for the partial melting of rocks, and initiating magma generation. The heat transfer to the lithosphere is considered to be governed mainly by the convective motion inside the asthenosphere. In order to mathematically describe this process, a generalization of a nonlinear convective 1D model, possibly representing a useful though simplified model for the birth of a volcano, and already analyzed from an analytical viewpoint (Godano et al., 2022), is investigated; here, we solve numerically some physically meaningful initial and boundary value problems, and discuss the results.