Modeling 3D Magma Dynamics Using a Discontinuous Galerkin Method (Communications in Computational Physics, 2018)
Discontinuous Galerkin (DG) and matrix-free finite element methods witha novel projective pressure estimation are combined to enable the numerical modelingof magma dynamics in 2D and 3D using the library deal.II. The physical modelis an advection-reaction type system consisting of two hyperbolic equations to evolveporosity and soluble mineral abundance at local chemical equilibrium and one ellipticequation to recover global pressure. A combination of a discontinuous Galerkinmethod for the advection equations and a finite element method for the elliptic equationprovide a robust and efficient solution to the channel regime problems of thephysical system in 3D. A projective and adaptively applied pressure estimation is employedto significantly reduce the computational wall time without impacting the overallphysical reliability in the modeling of important features of melt segregation, suchas melt channel bifurcation in 2D and 3D time dependent simulations.