Depth-averaged unsteady RANS simulation of resonant shallow flows in lateral cavities using augmented WENO-ADER schemes

Abstract

Turbulent shallow flows are characterized by the presence of horizontal large-scale vortices, caused by local variations of the velocity field. Apart from these 2D large vortices, small scale 3D turbulence, mainly produced by the interaction of the flowing water with the solid boundaries, is also present. The energy spectrum of turbulent shallow flows shows the presence of a 2D energy cascade at low wave numbers and a 3D energy cascade at high wave numbers, with a well-defined separation region between them. Horizontal flow movements (e.g. 2D large-scale vortical structures) at low wave numbers mostly determine the hydrodynamic behavior of these flows. Moreover, the generation of standing waves often occurs closely associated to the interaction of 2D horizontal flows with lateral boundaries, this is the case of seiches. To adequately reproduce these phenomena, a mathematical and numerical model able to resolve 2D turbulence is required. We herein show that depth-averaged (DA) unsteady Reynolds averaged Navier Stokes (URANS) models based on the Shallow Water Equations (SWE) are a suitable choice for the resolution of turbulent shallow flows with sufficient accuracy in an affordable computational time. The 3D small-scale vortices are modelled by means of diffusion terms, whereas the 2D large-scales are resolved. A high order numerical scheme is required for the resolution of 2D large eddies. In this work, we design a DA-URANS model based on a high order augmented WENO-ADER scheme. The mathematical model and numerical scheme are validated against observation of complex experiments in an open channel with lateral cavities that involve the presence of resonant phenomena (seiching). The numerical results evidence that the model accurately reproduces both longitudinal and transversal resonant waves and provides an accurate description of the flow field. The high order WENO-ADER scheme combined with a SWE model allows to obtain a powerful, reliable and efficient URANS simulation tool.

Drivers for mass and momentum exchange between the main channel and river bank lateral cavities

“…A thorough design of the geometry of such local widenings in a river reach is needed in terms of their impact on the channel hydrodynamics (Valentine and Wood [9], Uijttewaal et al [10], Weitbrecht et al [11], Lesack and Marsh [12], Sukhodolov [13], Akutina [14], Mignot et al [15], Navas-Montilla et al [16]) and on the transport of such environmental variables as fine sediments (Juez et al [17,18]), pollutants, oxygen and nutrients (Jackson et al [19,20], Sanjou et al [21]). As a result, numerous field, laboratory and numerical studies were carried out to elucidate the mass and momentum exchange mechanisms between the main flow and the lateral cavities.…”

Modelos de simulación de alto orden para la resolución de fenómenos de propagación de ondas en flujos de lámina libre con turbulencia

“…La turbulencia en flujos de aguas poco profundas se caracteriza por la coexistencia de dos escalas diferenciadas de estructuras turbulentas: turbulencia 2D horizontal de gran escala y turbulencia 3D de pequeña escala, como se muestra en la figura 3 (Nadaoka y Yagi, 1998;Navas-Montilla et al, 2019). Dado que el modelo matemático que representa el flujo es un modelo 2D (promediado en la vertical), es posible resolver la turbulencia 2D de gran escala, mientras que habrá que modelar la turbulencia 3D de pequeña escala.…”

“…Así, la metodología WENO-ADER se utiliza para generar un modelo URANS (Unsteady Reynolds Averaged Navier Stokes) que permite resolver los vórtices horizontales con precisión e incluir el efecto de la turbulencia 3D no resuelta. El esquema se ha validado utilizando distintos casos test que involucran la generación y transporte de estructuras turbulentas bidimensionales (Navas-Montilla et al, 2019).…”

Simplified Spectral Model of 3D Meander Flow

“…The balance of the numerical efficiency and accuracy for hydrodynamic modeling drives the balanced treatment of different physical processes [23,24]. Recently, Navas-Montilla et al [25] solved the shallow water equations with a high-order WENO-ADER scheme, which shows great potential for modeling meander flows with secondary currents with these novel methods.…”