In this work a preliminary analysis is carried out, concerning the numerical integration of shallow water equations on movable bed. The fundamental aim is to understand if it is possible to capture the main features of some typical meso-scale bedforms, namely river dunes and/or antidunes, through a depth averaged approach, avoiding the numerical integration of full Navier-Stokes Equations by means of RANS or LES approach. The analysis regards the typical range of fluvial hydraulics, that is low sediment transport rate and negligible collisional effects between solid grains. The governing equations are the mass and momentum balance in the shallow water frame and the Exner equation for the bed elevation. Some classical results, considered as stated by the literature on this topic, are taken into account, namely the effects of the skin fiction and of the local bottom slope on the sediment mobility, the key parameter to evaluate the bed load transport. A source of uncertainties is the separation between the form drag effect and the skin friction effect in evaluating the total friction in a bedform-covered alluvial bottom. In order to separate such effects, we remove the average longitudinal bed slope from the momentum equation, and it is idealized as the external forcing which establishes the average mean flow in the considered domain. Firstly, a quasi-analytical approach is adopted, considering as small the sediment discharge with respect to the liquid discharge. The flux matrix eigenvalues and eigenvectors are found, and it is shown how sediment transport affects bedforms celerity and Riemann invariants. Secondly, a relaxation approach is proposed, to take properly into account the bedload time-adaptation to the local hydrodynamic conditions. In both cases, numerical computations are carried out using the Dumbser-Toro extension of the Osher Riemann Solver to non-conservative hyperbolic systems, in order to properly take into account the role of the bottom elevation as time-space variable. Some examples are shown, in typical range of existence of real river bedforms.

### Some results on the numerical treatment of Movable Bed Shallow Water Equations

#### Abstract

In this work a preliminary analysis is carried out, concerning the numerical integration of shallow water equations on movable bed. The fundamental aim is to understand if it is possible to capture the main features of some typical meso-scale bedforms, namely river dunes and/or antidunes, through a depth averaged approach, avoiding the numerical integration of full Navier-Stokes Equations by means of RANS or LES approach. The analysis regards the typical range of fluvial hydraulics, that is low sediment transport rate and negligible collisional effects between solid grains. The governing equations are the mass and momentum balance in the shallow water frame and the Exner equation for the bed elevation. Some classical results, considered as stated by the literature on this topic, are taken into account, namely the effects of the skin fiction and of the local bottom slope on the sediment mobility, the key parameter to evaluate the bed load transport. A source of uncertainties is the separation between the form drag effect and the skin friction effect in evaluating the total friction in a bedform-covered alluvial bottom. In order to separate such effects, we remove the average longitudinal bed slope from the momentum equation, and it is idealized as the external forcing which establishes the average mean flow in the considered domain. Firstly, a quasi-analytical approach is adopted, considering as small the sediment discharge with respect to the liquid discharge. The flux matrix eigenvalues and eigenvectors are found, and it is shown how sediment transport affects bedforms celerity and Riemann invariants. Secondly, a relaxation approach is proposed, to take properly into account the bedload time-adaptation to the local hydrodynamic conditions. In both cases, numerical computations are carried out using the Dumbser-Toro extension of the Osher Riemann Solver to non-conservative hyperbolic systems, in order to properly take into account the role of the bottom elevation as time-space variable. Some examples are shown, in typical range of existence of real river bedforms.
##### Scheda breve Scheda completa Scheda completa (DC)
2014
Shallow Water Equations; Sediment Transport; Movable Bed; Non-conservative Hyperbolic Systems
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11392/1981412`
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