ABSTRACT
The computational simulation of hydro- and morphodynamic processes and the development of adapted numerical methods is currently a wide field of research. Especially morphological models normally assume subcritical flow (Vasquez, Millar & Steffler, 2005). Phenomena like antidunes cause numerical instabilities because the bed celerity is opposite the direction of sediment transport.
(Volp, Prooijen, Pietrzak & Stelling, 2015) presents a new upwind scheme to improve simulation of bed propagation. The presented method provides upwind direction based on the bed celerity cD (see eq. 1). () c D = Δ q S Δ z B = q S , 2 − q S , 1 z B , 2 − z B , 1 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315623207/4fbc492d-6678-4a12-aaf6-5c2b8ea38e5f/content/eq969.tif"/>
ΔqS differenz of the transport capacity
ΔhB bottom slope parameter
This improvement ensures numerical stability for both ratios shown in figure 1. In the upper graph, transport rate increases through the shallow area. Therefore transport capacity of the upstream cell has to be taken. Figure 1b shows decreasing transport capacity in the second cell, so upstream direction has to contrary. 2D flow through a channel with shallow area. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315623207/4fbc492d-6678-4a12-aaf6-5c2b8ea38e5f/content/fig128_1.tif"/>
The improvement of the outlined scheme has already been demonstrated for sub-critical flow using various test cases (e.g. Gaussian cone). This paper will include the method to the morphological model SediMorph (Malcherek, Piechotta & Knoch, 2005) and expand theory to super-critical flow.
The physical concept is validated by the numerical critical test case of an anti-dune. In result numerical instabilities are prevented and the simulation of propagation will be opposite the direction of flow.
As a generally valid upwind scheme, this method represents a significant enhancement on convenional schemes and should be standard for morphological models.
