SUMMARYIn this paper, finite elements based on arbitrary convex and non-convex polytopes are introduced. Polytopes in combination with natural element coordinates (NECs) permit a uniform element formulation of interpolation functions that are independent of the dimension of space, localization and the number of vertices. NECs based on the natural neighbor interpolation are restricted to the polytope and can be understood as an extension of the barycentric coordinates on simplexes. The differentiation and integration of these interpolation functions on the basis of NECs is essential for finite element approximations.The accuracy of the finite element interpolation or approximation can be controlled by either applying the h-version or by utilizing the p-version of the finite element method (FEM). Advantages in the handling of hanging nodes are discussed. Furthermore, we present construction methods for Lagrangian as well as for hierarchical interpolation functions based on NECs.Numerical experiments on different convex and non-convex decompositions will show the usability, accuracy and convergence of the developed polytope FEM.
<p>With an area of almost 10,000 km&#178;, the project area represents the tidal flats on Germany&#8217;s North Sea coast. The tidal flats and their channels as well as morphologically highly active estuarine systems undergo significant erosional and sedimentational processes that prove difficult the assessment of sedimentological composition based on relatively few and temporally far stretched field measurements. The holistic databased simulation of both the internal structure of the soil itself and its sedimentary composition is based on around 21,000 measured surface sediment samples (from 1949 until recent) and yearly consistent digital bathymetric models, starting 1950, spatiotemporally interpolated in a 10 m grid resolution by the Functional Seabed Model. By utilizing the high temporal and spatial resolution of the bathymetric models, it is possible to quantify the seabed depth evolution (sedimentation and erosion) and to solve a differential equation to capture sedimentary evolution, a consistent and continuous three dimensional model of both the surface and the subsurface structures and sedimentary compositions can be generated. To further extend the volumetric extent of the model, around 16,000 sedimentary core samples are used to fill the spatial and consequently the temporal void between the lowest altitudinal range of validity of the aforementioned model segment to the lower boundary of the target model volume. This boundary is set to be the lower limit of the morphologically active or activatable space, which contains the volume of sediment that could be eroded in current climate conditions. The limit, generally speaking, can be expected to somewhat coincide with the base of Holocene sediments, as Pleistocene sediments &#8211; especially subglacial tills &#8211; generally take higher amounts of bottom shear stress to erode than unindurated Holocene sediments, which usually form tidal flat sediments. The purpose of the generated three dimensional model is to be able to derive sedimentological information in both custom spatial resolution as well as custom sedimentological classification as base and validation data for process based morphodynamic simulation models. With these enhanced models, the quality of the prognosis of morphological developments and stability of coastal areas as a tool for planning processes for coastal protection and maritime economy is expected to be increased.</p>
Abstract. The German Bight located within the central North Sea is a hydro- and morphodynamically highly complex system of estuaries, barrier islands and part of the world’s largest coherent tidal flats, the Wadden Sea. To identify and understand challenges faced by coastal stakeholders, such as harbor operators or governmental agencies, to maintain waterways and employ numerical models for further analyses, it is imperative to have a consistent data base for both bathymetry and surface sedimentology. Current commercial and public data products are insufficient in spatial and temporal 15 resolution and coverage for recent analyses methods. Thus, this first part of a two-part publication series of the German joint project EasyGSH-DB describes annual bathymetric digital terrain models in a 10 m gridded resolution for the German North Sea coast and German Bight from 1996 to 2016 (Sievers et al., 2020a, https://doi.org/10.48437/02.2020.K2.7000.0001), as well as surface sedimentological models of discretized cumulative grain size distribution functions for 1996, 2006 and 2016 on 100 m grids (Sievers et al., 2020b, https://doi.org/10.48437/02.2020.K2.7000.0005). Furthermore, basic morphodynamic and sedimentological 20 processing analyses, such as the estimation of e.g. bathymetric stability or surface maps of sedimentological parameters, are provided (Sievers et al., 2020a, 2020b, see respective download links).
The consideration of biological processes in hydro-and morphodynamic models is an important challenge for numerical simulation in coastal engineering. Eco-hydraulic aspects will play a major role in engineering tools and planning processes for the design of coastal works. Vegetation greatly affects the hydro-and morphodynamic models in coastal zones. Most hydrodynamic numerical models do not consider influences by ecological factors. This paper focuses on the presentation of an object-oriented holistic framework for ecohydraulic simulation. The numerical approximation is performed by a stabilized finite element method for hydro-and morphodynamic processes, to solve the related partial differential equations, and by a cell-oriented model for the simulation of ecological processes, which is based on a fuzzy rule system. The fundamental differences between these model paradigms require special transfer and coupling methods. Case studies on seagrass prediction in the North Sea around the island of Sylt show the main effects and influences on changed hydro-and morphodynamic processes and demonstrate the applicability of the coupled finite element fuzzy cell-based approach in eco-hydraulic modeling.
Abstract. The German Bight located within the central North Sea is a hydro- and morphodynamically highly complex system of estuaries, barrier islands, and part of the world's largest coherent tidal flats, the Wadden Sea. To identify and understand challenges faced by coastal stakeholders, such as harbor operators or governmental agencies, to maintain waterways and employ numerical models for further analyses, it is imperative to have a consistent database for both bathymetry and surface sedimentology. Current commercial and public data products are insufficient in spatial and temporal resolution and coverage for recent analysis methods. Thus, this first part of a two-part publication series of the German joint project EasyGSH-DB describes annual bathymetric digital terrain models at a 10 m gridded resolution for the German North Sea coast and German Bight from 1996 to 2016 (Sievers et al., 2020a, https://doi.org/10.48437/02.2020.K2.7000.0001), as well as surface sedimentological models of discretized cumulative grain size distribution functions for 1996, 2006, and 2016 on 100 m grids (Sievers et al., 2020b, https://doi.org/10.48437/02.2020.K2.7000.0005). Furthermore, basic morphodynamic and sedimentological processing analyses, such as the estimation of, for example, bathymetric stability or surface maps of sedimentological parameters, are provided (Sievers et al., 2020a, b, see respective download links).
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