A depth-averaged non-cohesive sediment transport model with improved discretization of flux and source terms

Abstract

This paper presents novel flux and source term treatments within a Godunov-type finite volume framework for predicting the depthaveraged shallow water flow and sediment transport with enhanced the accuracy and stability. The suspended load ratio is introduced to differentiate between the advection of the suspended load and 1 the advection of water. A modified Harten, Lax and van Leer Riemann solver with the contact wave restored (HLLC) is derived for the flux calculation based on the new wave pattern involving the suspended load ratio. The source term calculation is enhanced by means of a novel splitting-point implicit discretization. The slope effect is introduced by modifying the critical shear stress, with two treatments being discussed. The numerical scheme is tested in five examples that comprise both fixed and movable beds. The model predictions show good agreement with measurement, except for cases where local three-dimensional effects dominate. sediment transport; total load model; HLLC Riemann solver; finite-volume method; source term treatment Highlights 1. A second-order finite-volume method is presented for solving the total-load sediment transport 2. An improved HLLC Riemann solver is derived 3. An improved bed slope treatment is derived to account for density variation inside the cell 4. A novel implicit source term discretization is presented 5. The numerical model shows good agreement with measurement as long as the shallow flow assumptions are valid 2

Layered shallow water equations: Spatiotemporally varying layer ratios with specific adaptation to wet/dry interfaces

“…1 Firstly the ratio (𝛾 𝛼 ) of each layer depth h 𝛼 to total flow depth ∑ N 𝛽=1 h 𝛽 remains constant throughout the domain length, and the exchange terms along with shear stresses are minimal. Similar treatments for non-conservative terms have been previously used by Kim and LeVeque, 2009 8 and Zhao, et al, 2019, 35 where the system relies on the assumption of a strong advective terms, and the source/sink term(s) are excluded in the calculation of the jacobian. The state variable and the flux term can then be written as follows:…”

“…The right eigenvector of the system of equations for two generalized adjacent layers is utilized to show the mutual independence of the flux calculations for both. The Riemann invariants of the system 36,37 are presented as follows:…”

“…] throughout the domain. An additional term appears in form of temporal gradient as depicted in Equation (35).…”

Discrete Boltzmann Numerical Simulation of Simplified Urban Flooding Configurations Caused by Dam Break

“…In the last decades, great attention has been paid to the development of numerical solvers for the SWE (Toro and Garcia-Navarro, 2007;Toro, 2009). The latter tackle directly the SWE by means of the finite volumes discretization and have reached a sufficient level of complexity so that they are able to account for crucial issues such as to cite just a few, the treatment of topography source terms (Duran and Marche, 2014;Hou et al, 2018), the use of unstructured grids (Zhao et al, 2019), and the evolution of wet-dry fronts (Ferrari et al, 2019).…”

Discontinuous Galerkin methods for a dispersive wave hydro-sediment-morphodynamic model

“…Cao et al [17] use the total-variation-diminishing (TVD) weighted average flux method (WAF) in conjunction with the Harten-Lax-van Leer-contact (HLLC) approximate Riemann solver to develop their numerical solution algorithm for the SHSM equations. Examples of works that employ HLLC as an approximate Riemann solver for numerical flux definitions include [18], [19], and [20]. Algorithms based on upwinding numerical fluxes and Roe-averaged states are developed in [21] and [22].…”