Modeling Magma Dynamics with a Mixed Fourier Collocation - Discontinuous Galerkin Method (Communications in Computational Physics, 2011)
A high-order discretization consisting of a tensor product of the Fourier collocationand discontinuous Galerkin methods is presented for numerical modeling ofmagma dynamics. The physical model is an advection-reaction type system consistingof two hyperbolic equations and one elliptic equation. The high-order solutionbasis allows for accurate and efficient representation of compaction-dissolution wavesthat are predicted from linear theory. The discontinuous Galerkin method providesa robust and efficient solution to the eigenvalue problem formed by linear stabilityanalysis of the physical system. New insights into the processes of melt generationand segregation, such as melt channel bifurcation, are revealed from two-dimensionaltime-dependent simulations.