A wetting and drying algorithm with a combined pressure/free-surface formulation for non-hydrostatic models |
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| Authors: | SW Funke CC Pain SC Kramer MD Piggott |
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| Institution: | aApplied Modelling and Computation Group, Department of Earth Science and Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK;bGrantham Institute for Climate Change, Imperial College London, South Kensington Campus, London SW7 2AZ, UK |
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| Abstract: | A wetting and drying method for free-surface problems for the three-dimensional, non-hydrostatic Navier–Stokes equations is proposed. The key idea is to use a horizontally fixed mesh and to apply different boundary conditions on the free-surface in wet and dry zones. In wet areas a combined pressure/free-surface kinematic boundary condition is applied, while in dry areas a positive water level and a no-normal flow boundary condition are enforced. In addition, vertical mesh movement is performed to accurately represent the free-surface motion. Non-physical flow in the remaining thin layer in dry areas is naturally prevented if a Manning–Strickler bottom drag is used. The treatment of the wetting and drying processes applied through the boundary condition yields great flexibility to the discretisation used. Specifically, a fully unstructured mesh with any finite element choice and implicit time discretisation method can be applied. The resulting method is mass conservative, stable and accurate. It is implemented within Fluidity-ICOM 1] and verified against several idealized test cases and a laboratory experiment of the Okushiri tsunami. |
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| Keywords: | Wetting and drying Non-hydrostatic Navier&ndash Stokes equations Finite element method Implicit time integration |
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