A nonlinear model for acoustic-gravity waves

This project concerns nonlinear mathematical models and accurate numerical methods, for reliable prognosis of nonlinear acoustic-gravity waves from seismic events, such as volcanic eruptions.

This project is divided into 3 tasks:1) Develop a nonlinear 3D model of the atmosphere coupled through topography to a solid medium, modelled by the 3D elastic wave equation. The nonlinear model must account for irregular topography.

The governing equations in the atmosphere are essentially the compressible Navier-Stokes equations with addition of volcanic forcing and gravity. 2) Develop a numerical method that accurately solves the coupled system in collaboration with Stanford University and SMHI. The numerical method should handle strong nonlinear effects such as shock waves, but also the fluid-solid interaction.

The numerical method, based on high-order accurate finite difference schemes, should also incorporate efficient absorbing boundary conditions.3) Incorporation of a nonlinear 3D eruption model, that describes both magma flow during eruption and perturbations about that flow, in collaboration with Stanford University.

The eruption model will couple both to the solid medium and to the nonlinear atmosphere.

These couplings will allow us to capture both the nonlinear generation and propagation of nonlinear acoustic-gravity waves and linear elastic waves from volcanic eruptions. The fully coupled problem allows for inverse modeling of the active magma transport system.