Computers and Fluids 166 (2018) 275–285 Contents lists available at ScienceDirect Computers and Fluids journal homepage: www.elsevier.com/locate/compfuid Numerical simulation of the temporal evolution of a three dimensional barchanoid dune and the corresponding sediment dynamics M. Burkow a,∗ , M. Griebel a,b a Institute for Numerical Simulation, University of Bonn, Wegelerstrasse 6, Bonn 53115, Germany b Fraunhofer-Institut für Algorithmen und Wissenschaftliches Rechnen SCAI, Schloss Birlinghoven, Sankt Augustin 53754, Germany a r t i c l e i n f o Article history: Received 13 March 2017 Revised 14 November 2017 Accepted 14 February 2018 Available online 21 February 2018 Keywords: Numerical simulation Sediment transport Barchanoid dune CFD a b s t r a c t In this paper we present the results of the numerical simulation of a three-dimensional current-driven sediment transport process. In detail, the temporal evolution of a barchanoid dune is studied. Two phe- nomena are treated in this context. First, the three-dimensional flow of a single phase fluid is considered. Second, the interaction of the flow and the sediment bed with its morphological change of the sedi- ment surface is taken into account. We numerically solve the instationary incompressible Navier–Stokes equations, an advection diffusion equation and Exner’s bed level equation to update the sediment bed morphology. Here, Exner’s equation determines the change of the bed level due to the bed load. The sus- pended material is treated as a sediment concentration and its movement is modelled by an advection- diffusion equation. To secure the continuous interchange between bed load and the suspension load sink and source terms are used. Both equations are discretised and explicitly coupled to the discrete fluid model. The typical sedimentary processes and the sedimentary form of a prototypical barchanoid dune are well captured by our numerical simulation, which is supported by a qualitative comparison with ex- amples from the literature. © 2018 Elsevier Ltd. All rights reserved. 1. Introduction Sediment transport processes and their effects on the morphol- ogy of the sediment bed are significant issues in hydraulic engi- neering. Usually, the physical processes of the formation of dunes and other sedimentary forms are studied in laboratory flumes or in field experiments. These time-intensive and costly studies are not always easy to conduct. At this point, a numerical simulation can help to reduce costs and to provide more insight and therefore a better understanding of the relevant flow and transport phenom- ena. There are different classifications of dunes in the aeolian regime as well as in the fluvial regime. For example, linear dunes, cres- cent shaped dunes, e.g. parabolic or barchanoid dunes, and star shaped dunes demonstrate the large diversity of dune forms. Here, the availability of sand, its consistency, the predominant wind sit- uation and many other factors determine the dune type, compare [24]. In general, the sediment is transported in the bed load layer over the dune body upwards the upstream slope. When the sand particles are transported to the top end of the dune, the particles slide down the downstream slope, which is limited by the angle of ∗ Corresponding author. E-mail address: burkow@ins.uni-bonn.de (M. Burkow). repose. In case of a barchanoid dune, the transport velocities are higher near the lateral ends of the dune body. This fact leads to a faster transport of the sand at the sides of the dune body and to the development of sand horns, which are transported further downstream. The resulting dune body and the involved processes are strictly three-dimensional. We present a numerical approach for their simulation and discuss the obtained results. The remainder of this paper is organised as follows. In Section 2, we describe the full fluid-sediment-model, which con- sists of the Navier–Stokes equations, a suspension load model, and Exner’s bed level equation. In Section 3, we shortly discuss our nu- merical discretisation and its properties. In Section 4, we present the results of our numerical simulation for the temporal evolution of a barchanoid dune. A conclusion is given in the fifth section. 2. Model: Navier–Stokes, sediment transport and surface model The used model comprises a three-dimensional fluid model and the sediment equations, which realise the suspension load trans- port and the morphological change of the sediment surface. Parts of the presented models were previously studied in the litera- ture, e.g. [17,23,33–35,41]. Some authors already combined a two or three dimensional fluid solver with a sediment model for the morphological change ([4,34,35]) or the suspension load [5,41]. https://doi.org/10.1016/j.compfluid.2018.02.018 0045-7930/© 2018 Elsevier Ltd. All rights reserved.