Towards modelling magmatic systems using a staggered grid finite difference method

The dynamics of magmatic systems remain poorly understood, due to the lack of resolving power of geophysical methods to study active systems and the difficulty of interpreting exposed crystallized magma bodies. Numerical models are therefore helpful to connect the dots between classical geological studies, using rheological information and geometries derived from field or geophysical investigations to shed new lights on the mechanisms involved in such systems.

Taking advantage of the big CPU clusters currently available and the development of the DMStag framework as part of the PETSc infrastructure, the ERC-funded MAGMA project aims to build tools to analyse magmatic processes in the lithosphere. We developed a finite-difference staggered grid code solving the Stokes equations for visco-elasto-plastic rheologies and using analytical jacobians for linear and non-linear solvers, combined with regularized plasticity. The code is combined with both a marker and cell and semi-lagrangian advection schemes, is fully parallel and includes automated testing.

Here, we provide application examples ranging from simple benchmark validations against analytical solutions to more complex settings taking advantage of the broad rheologies and local heterogeneities permitted by high resolution settings and the finite difference method. Ongoing technical developments include adding two-phase flow and coupling to it with thermodynamic calculations to track the evolving chemistry of magmatic systems.