Evaluation of methods for numerical simulation of wetting and drying in shallow water flow models

Ten methods for numerical simulation of wetting and drying in two-dimensional shallow water flow models, including three new ones, are reviewed and evaluated in this paper. The methods are also applicable to three-dimensional hydrostatic barotropic models based on natural coordinates. The target method should have the following properties: (i) work in implicit schemes with sufficiently large time steps; (ii) work on Arakawa-C grid with piecewise bilinear ground levels defined on cell sides; (iii) no excessive wiggles produced by irregular wetting and drying; and (iv) global and local mass conservation. A taxonomy of the methods is first introduced, relevant to: (i) the criterion for the declaration of the wet or dry status of the cells in the computational mesh, (ii) the effective evaluation of the retention volume in each cell, and (iii) the computation of water depth between two adjacent cells. Seven existing methods are then checked with test cases of increasing difficulty. By means of simple 1D tests, unphysical behaviours are shown arising from the most common way of computing water depths between cells, as well as from the effective evaluation of the cell retention volume. Three new methods are then introduced to cope with these problems. Also, two methods originally proposed for a different ground model show a major inconsistency with the present ground model and are thus excluded from further comparisons. The eight remaining methods are then checked by means of a severe 2D test case for which an analytical solution is known. Of the three new methods, two proved particularly suitable for practical applications in long-term computations, while the third, besides yielding the most accurate solution, is quite time consuming. (C) 1998 Elsevier Science B.V. All rights reserved.