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# Mass conservation in computational morphodynamics: uniform sediment and infinite availability

Authors:
DOI:
10.1002/fld.4015
Abstract:
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 Open 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.
Type:
Journal article
Language:
English
Published in:
International Journal for Numerical Methods in Fluids, 2015, Vol 78, Issue 4, p. 233-256
Keywords:
Exner equation; Unstructured finite volume; Dual mesh; Interpolation scheme; Geometric sand slide
Main Research Area:
Science/technology
Publication Status:
Published
Review type:
Peer Review
Submission year:
2015
Scientific Level:
Scientific
ID:
274799377