A free surface capturing discretization for the staggered grid finite difference scheme

Abstract

International audienceThe coupling that exists between surface processes and deformation within both the shallowcrust and the deeper mantle-lithosphere has stimulated the development of computationalgeodynamic models that incorporate a free surface boundary condition. We introduce a treatmentof this boundary condition that is suitable for staggered grid, finite difference schemesemploying a structured Eulerian mesh. Our interface capturing treatment discretizes the freesurface boundary condition via an interface that conforms with the edges of control volumes(e.g. a ‘staircase’ representation) and requires only local stencil modifications to be performed.Comparisons with analytic solutions verify that the method is first-order accurate. Additionalintermodel comparisons are performed between known reference models to further validateour free surface approximation. Lastly, we demonstrate the applicability of a multigrid solverto our free surface methodology and demonstrate that the local stencil modifications do notstrongly influence the convergence of the iterative solver