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

Thibault Duretz (1) , D.A. May (2) , Philippe Yamato (3)

1 Institute of Geology and Palaeontology
2 Institute of Geophysics [ETH Zürich]
3 GR - Géosciences Rennes

The coupling that exists between surface processes and deformation within both the shallow crust and the deeper mantle-lithosphere has stimulated the development of computational geodynamic models that incorporate a free surface boundary condition. We introduce a treatment of this boundary condition that is suitable for staggered grid, finite difference schemes employing a structured Eulerian mesh. Our interface capturing treatment discretizes the free surface 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. Additional intermodel comparisons are performed between known reference models to further validate our free surface approximation. Lastly, we demonstrate the applicability of a multigrid solver to our free surface methodology and demonstrate that the local stencil modifications do not strongly influence the convergence of the iterative solver.

Keywords: Numerical solutions; Dynamics of lithosphere and mantle; Mechanics; theory; and modelling.

Domains: Tectonics

Thibault Duretz, D.A. May, Philippe Yamato. A free surface capturing discretization for the staggered grid finite difference scheme. Geophysical Journal International, 2016, 204 (3), pp.1518-1530. ⟨10.1093/gji/ggv526⟩. ⟨insu-01271289⟩