Mass conservation in computational morphodynamics: uniform sediment and infinite availability

Abstract

SUMMARYComputational 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 OpenFOAM. Furthermore, effects from horizontal displacements of the vertices, explicit filtering of the evolving bed and morphological acceleration on global mass conservation, are discussed.

Numerical simulation of scour and backfilling processes around a circular pile in waves

“…The mesh is updated each time the bed is updated. The method applied in this work has a slight mass conservation error as shown in Jacobsen (2015). This mass conservation error was estimated from the numerical results and it was found neither to impact the results qualitatively nor quantitatively.…”

“…In the case of waves, Uf in the above equation is the phase-resolved instantaneous friction velocity. Throughout the present work, the coefficient of dynamic friction is set to μd =0.51 (Fredsøe and Deigaard,1992, p.218) and the reference level is taken as b=α1d=3.5d (Fuhrman et al,2014;Baykal et al 2014;2015).…”

A Comparison of Different Wave Modelling Techniques in An Open-Source Hydrodynamic Framework

“…Wave breaking takes place when the ratio between the free surface elevation difference and the horizontal distance difference at adjacent cells is higher than the criterion, which has a default value of 1.25. A filtering scheme is used to smooth the free surface in order to dissipate wave energy when wave breaking is detected [54].…”

Vertical dependences in swash-zone flows and sand transport

“…pointing into the ground). The calculation of these fluxes as they occur in the cells of the discretised domain are described in more detail in Jacobsen et al (2014) and Jacobsen (2015). The sandsliding mechanism is activated when the bed slope exceeds the critical bedslope β c .…”

“…This bed level change is then applied using a moving mesh, which moves the mesh points such that the boundary displacement corresponds to the calculated morphological change. This is done using the mass conserving interpolation method by Jacobsen (2015).…”