Numerical modeling of magma-repository interactions

This report explains the numerical programs behind a comprehensive modeling effort of magma-repository interactions. Magma-repository interactions occur when a magma dike with high-volatile content magma ascends through surrounding rock and encounters a tunnel or drift filled with either a magmatic gas or air at atmospheric pressure. The simplified mathematical model to describe these flow phenomena consists of compressible flow equations of one- or two-dimensional flow in a flow tube with a macroscopic equation of state relating the pressure to the density for a bubbly mixture of water in the liquid or vapor phase and the molten rock under isothermal conditions. These model equations are hyperbolic and consist of a conservative part and additional frictional and geometric terms. The latter geometric terms contain the influence of the varying cross section or width of the flow tube, and gravity. Two shock-capturing numerical methods, a Local Lax Friedrichs and an Essentially Non-Oscillatory scheme, are used to simulate these flows numerically. An extensive account is given of these two numerical methods and their validation for the magma flow application, including a comparison between various exact solutions and numerical solutions for idealized conditions. Finally, we give one- and two-dimensional reference simulations in more realistic flow geometries.