NUMERICAL SIMULATION OF DISPERSIVE MAGMA SHOCK WAVES

Developing a rigorous computational approach to problems involving magma transport has been of interest to the geophysical community for some time. Interactions between magma and a permeable, deformable medium, representing a solid matrix or a different melt with larger viscosity, can produce dispersive shock waves (DSWs) connecting two disparate porosity states. DSWs are composed of an expanding, oscillatory wave packet with a large amplitude soliton leading edge. Long integration times and high spatial resolution are required to properly resolve DSWs. In this work, the McKenzie magma equations are solved numerically using high order finite difference methods. Simulations of one-dimensional DSW formation resulting from an initial step in matrix porosity are performed and compared with asymptotic DSW theory resulting in parameter estimates for DSW amplitude and leading/trailing edge velocities. This code extends the scope of previous models by accommodating a larger range of melt permeability and bulk viscosity constitutive relations.