Bed Evolution under Rapidly Varying Flows by a New Method for Wave Speed Estimation

Abstract

This paper proposes a sediment-transport model based on coupled Saint-Venant and Exner equations. A finite volume method of Godunov type with predictor-corrector steps is used to solve a set of coupled equations. An efficient combination of approximate Riemann solvers is proposed to compute fluxes associated with sediment-laden flow. In addition, a new method is proposed for computing the water depth and velocity values along the shear wave. This method ensures smooth solutions, even for flows with high discontinuities, and on domains with highly distorted grids. The numerical model is tested for channel aggradation on a sloping bottom, dam-break cases at flume-scale and reach-scale with flat bottom configurations and varying downstream water depths. The proposed model is tested for predicting the position of hydraulic jump, wave front propagation, and for predicting magnitude of bed erosion. The comparison between results based on the proposed scheme and analytical, experimental, and published numerical results shows good agreement. Sensitivity analysis shows that the model is computationally efficient and virtually independent of mesh refinement.

The Linearity of the Euler Equation as a Result of the Compressibility of a Fluid

“…Substituting (9), (11), (14) and (21) in the boundary conditions (19), we will get the system of homogenous equations referred to unknown coefficients…”

Dam-Break Flows: Comparison between Flow-3D, MIKE 3 FM, and Analytical Solutions with Experimental Data

“…Developments from past studies have provided several numerical models aimed at solving the so-called dam break flooding problem [16], and one-dimensional models, such as Hec-Ras, DAMBRK and MIKE 11,etc. have been used to model dam-break flooding [17]. Two-dimensional (2D) depth-averaged equations have also been widely used to simulate the dam-break flow problem [18][19][20][21][22], and the results show that shallow water equations (SWE) are suitable for representing fluid flows. However, in some cases, the solutions provided by 2D numerical solvers may not be consistent with the experiments, particularly in the near field [23,24].…”

Correct Definition of Sound Speed and Its Consequences in the Tasks of Hydrodynamics

“…This is evidenced by the fact that they are scarcely cited. For example, we give several studies [7][8][9][10][11][12][13][14][15][16][17][18], published after 2012, and, as before, consider liquids as incompressible and their motion as potential. Work [12] is worthy of particular regret, as it represents lecture notes and is designed for students.…”