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

Abstract : 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.
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Submitted on : Thursday, February 11, 2016 - 8:16:20 AM
Last modification on : Monday, March 23, 2020 - 12:50:05 PM
Long-term archiving on: : Thursday, May 12, 2016 - 5:29:37 PM

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

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