The Face-Centered Finite Volume method for Geodynamic Modelling

The Face-Centered Finite Volume (FCFV) is a newly developed discretisation technique that has been applied to a variety of engineering problems. This approach is based on the hybridisable discontinuous Galerkin formulation with constant degree approximations. The FCFV is particularly attractive approach since it meets numerous essential criteria for successful geodynamic modelling. It offers full geometric flexibility, natural free surface boundary condition, second order accuracy velocity-field solutions, no oscillatory pressure modes, relatively low computational cost and adequate treatment of jump conditions at material interfaces. Here we present the implementation of Poisson and Stokes solvers in the Julia computing language. Here we present the implementation of Poisson and Stokes solvers using the performant Julia language. We discuss several solving strategies including direct-iterative and iterative pseudo-transient approaches, the latter executing efficiently on Graphical Processing Units. We extend the original FCFV Stokes formulation to account for discontinuous viscosity case and discuss the implementation of complex visco-elasto-plastic rheologies.