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Mass conservation in computational morphodynamics: uniform sediment and infinite availability
Author(s) -
Jacobsen Niels Gjøl
Publication year - 2015
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4015
Subject(s) - polygon mesh , beach morphodynamics , finite volume method , interpolation (computer graphics) , conservation of mass , unstructured grid , bed load , scalar (mathematics) , grid , mathematics , shallow water equations , sediment transport , mathematical optimization , computer science , geology , geometry , mechanics , sediment , mathematical analysis , physics , geomorphology , animation , computer graphics (images)
Summary Computational morphodynamics in finite volume methods are based on the evaluation of the rate of bed level change in the vertices on the deforming bed. With the use of finite volume methods on collocated (unstructured) grids, the rate of bed level change needs to be interpolated from the mesh faces to the vertices. First, this work reviews two methods based on a vectorial shape of the bed evolution equation (no scalar contributions from storage, erosion and deposition) in terms of their mass conserving properties. Second, a method that allows for scalar contributions in the bed evolution equation (the Exner equation) is proposed for general, unstructured meshes, and an analytical derivation for the simple one‐dimensional problem on a non‐equidistantly discretised grid is considered. The solution is compared with the general two‐dimensional formulation. The two‐dimensional formulation leads to the formulation of a geometric sand sliding routine on unstructured grids. The newly proposed interpolation method and the sand sliding routine are tested, and mass conservation of the sediment is considered with special emphasis on the effect of the solution accuracy for the suspended sediment transport. Discussions on other interpolation methods and their mass conserving properties are given with a special focus of the distance weighted interpolation method directly available and easily applied in O pen FOAM . Furthermore, effects from horizontal displacements of the vertices, explicit filtering of the evolving bed and morphological acceleration on global mass conservation, are discussed. Copyright © 2015 John Wiley & Sons, Ltd.