3d Compressible Melt Transport with Mesh Adaptivity

Melt generation and migration are important processes for the evolution of the Earth’s interior and impact the global convection of the mantle. While they have been the subject of numerous investigations, the typical time and lengthscales of melt transport are vastly different from global mantle convection, which determines where melt is generated. This makes it difficult to study mantle convection and melt migration in a unified framework. The equations that describe coupled Stokes-Darcy flow have been derived a long time ago and they have been successfully implemented and applied in numerical models. However, modeling magma dynamics poses the challenge of highly non-linear and spatially variable material properties, in particular the viscosity. In addition, previous models neglected the individual compressibilities of the solid and the fluid phase. However, experiments have shown that the melt density change from the depth of melt generation to the surface leads to a volume increase of up to 20%. Considering these volume changes in both phases also ensures self-consistency of models that strive to link melt generation to processes in the deeper mantle, where the compressibility of the solid phase becomes more important. Here, we describe our extension of the finite element mantle convection code ASPECT that adds equations describing the behavior of silicate melt percolating through and interacting with a viscously deforming host rock. We use the original compressible formulation of the McKenzie equations, augmented by an equation for the conservation of energy. This approach includes both melt migration and melt generation with the accompanying latent heat effects. Applying adaptive mesh refinement to this type of problems is particularly advantageous, as the resolution can be increased in mesh cells where melt is present and viscosity gradients are high, whereas a lower resolution is sufficient in regions without melt. Together with a high-performance, massively parallel implementation, this allows for high resolution, 3d, compressible, global mantle convection simulations coupled with melt migration. We evaluate the functionality and potential of this method using a series of benchmarks and model setups relevant for applications, compare results of the compressible and incompressible formulation and show the effectiveness of adaptive mesh refinement when applied to melt migration. Our model of magma dynamics provides a framework for modeling processes on different scales and investigating links between processes occurring in the deep mantle and melt generation and migration. This approach could prove particularly useful applied to modeling the generation of komatiites or other melts originating in greater depths. The ASPECT code, including all presented modifications, is available online under an Open Source license1