Source term treatment of SWEs using surface gradient upwind method

Pu, Jaan H.; Cheng, Nian‐Sheng; Tan, Soon Keat; Shao, Songdong

doi:10.1080/00221686.2011.649838

Cited by 46 publications

(33 citation statements)

References 29 publications

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“…A surface gradient upwind method (SGUM) for the numerical source terms treatment proposed by Pu et al [23] was integrated into this study to describe the combined operation of F and S in equation (13). The combination of F and S in the numerical iterations used in the SGUM could improve the numerical accuracy to predict the flow under different sediment transport conditions (including the investigated abutment bed scouring), since these conditions are heavily source terms bonded.…”

Section: Source Terms Schemementioning

confidence: 99%

“…It is worth mentioning that in Pu et al [23], the SGUM was only applied to the 1D water flow cases, but here it is used for the 2D SWEs model with sediment transport. With the application of SGUM, the MUSCL-Hancock scheme in equations (23) - (24) will become…”

Section: Source Terms Schemementioning

confidence: 99%

“…The slope limiter method was used in the HLLC solver to ensure the space discretization scheme satisfying the flux-limiting property. The source term of the proposed numerical scheme was modelled by a surface gradient upwind method (SGUM) as proposed by Pu et al [23].…”

Section: Numerical Schemementioning

confidence: 99%

“…Numerically, the monotonic upwind scheme of conservative laws (MUSCL)-Hancock scheme was used with the Harten Lax van Leer-contact (HLLC) approximate Riemann solver to discretize the FV model. The source terms of the numerical scheme was treated using a surface gradient upwind method (SGUM) originally proposed by Pu et al [23]. This method integrates the source term treatment into the inviscid discretization scheme using the upwind approach, and thus to enhance the simulation stability and accuracy for the heavily source terms affected bed scouring flow in this study.…”

Section: Introductionmentioning

confidence: 99%

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Efficient numerical computation and experimental study of temporally long equilibrium scour development around abutment

Lim

2013

Environ Fluid Mech

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For the abutment bed scour to reach its equilibrium state, a long flow time is needed. Hence, the employment of usual strategy of simulating such scouring event using the 3D numerical model is very time consuming and less practical. In order to develop an applicable model to consider temporally long abutment scouring process, this study modifies the common approach of 2D shallow water equations (SWEs) model to account for the sediment transport and turbulence, and provides a realistic approach to simulate the long scouring process to reach the full scour equilibrium. Due to the high demand of the 2D SWEs numerical scheme performance to simulate the abutment bed scouring, a recently proposed surface gradient upwind method (SGUM) was also used to improve the simulation of the numerical source terms. The abutment scour experiments of this study were conducted using the facility of Hydraulics Laboratory at Nanyang Technological University, Singapore to compare with the presented 2D SGUM-SWEs model.

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Section: Source Terms Schemementioning

confidence: 99%

Section: Source Terms Schemementioning

confidence: 99%

Section: Numerical Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficient numerical computation and experimental study of temporally long equilibrium scour development around abutment

Lim

2013

Environ Fluid Mech

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“…Ferreirra and Leal (1998), Yang and Greimann (1999), Brufau et al (2000) and more recently Xia et al (2010) had suggested that the effects of those two terms in equations (2) -(3) are insignificant in most sediment flow applications. For more source terms modelling information on the momentum equation, one could also refer to Pu et al (2012).…”

Section:  mentioning

confidence: 99%

Shallow sediment transport flow computation using time-varying sediment adaptation length

Hussain

Shao

et al. 2014

International Journal of Sediment Research

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YesBased on the common approach, the adaptation length in sediment transport is normally estimated in the temporal\ud independence. However, this approach might not be theoretically justified as the process of reaching of the sediment\ud transport equilibrium stage is affected by the flow conditions in time, especially for those fast sediment moving flows,\ud such as scour-hole developing flow. In this study, the 2D shallow water formulation together with a sediment\ud continuity-concentration (SCC) model were applied to flow with mobile sediment boundary. A time-varying approach\ud was proposed to determine the sediment transport adaptation length to treat the flow sediment erosion-deposition rate.\ud The proposed computational model was based on the Finite Volume (FV) method. The Monotone Upwind Scheme of\ud Conservative Laws (MUSCL)-Hancock scheme was used with the Harten Lax van Leer-contact (HLLC) approximate\ud Riemann solver to discretize the FV model. In the flow applications of this paper, a highly discontinuous dam-break\ud fast sediment transport flow was used to calibrate the proposed time-varying sediment adaptation length model. Then\ud the calibrated model was further applied to two separate experimental sediment transport flow applications\ud documented in literature, i.e. a highly concentrated sediment transport flow in a wide alluvial channel and a sediment\ud aggradation flow. Good agreements with the experimental data were presented by the proposed model simulations. The\ud tests prove that the proposed model, which was calibrated by the discontinuous dam-break bed scouring flow, also\ud performed well to represent the rapid bed change and the steady sediment mobility conditions.The National Natural Science Foundation of China NSFC (Grant Number 20101311246), Major State Basic Research Development Program (973 program) of China (Grant Number 2013CB036402) and Open Fund of the State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University of China (Grant Number SKLH-OF-1103)

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A finite element/volume method model of the depth‐averaged horizontally 2D shallow water equations

Yoshioka

Unami

Fujihara

2014

Numerical Methods in Fluids

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SUMMARYAnalysis of surface water flows is of central importance in understanding and predicting a wide range of water engineering issues. Dynamics of surface water is reasonably well described using the shallow water equations (SWEs) with the hydrostatic pressure assumption. The SWEs are nonlinear hyperbolic partial differential equations that are in general required to be solved numerically. Application of a simple and efficient numerical model is desirable for solving the SWEs in practical problems. This study develops a new numerical model of the depth‐averaged horizontally 2D SWEs referred to as 2D finite element/volume method (2D FEVM) model. The continuity equation is solved with the conforming, standard Galerkin FEM scheme and momentum equations with an upwind, cell‐centered finite volume method scheme, utilizing the water surface elevation and the line discharges as unknowns aligned in a staggered manner. The 2D FEVM model relies on neither Riemann solvers nor high‐resolution algorithms in order to serve as a simple numerical model. Water at a rest state is exactly preserved in the model. A fully explicit temporal integration is achieved in the model using an efficient approximate matrix inversion method. A series of test problems, containing three benchmark problems and three experiments of transcritical flows, are carried out to assess accuracy and versatility of the model. Copyright © 2014 John Wiley & Sons, Ltd.

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Source term treatment of SWEs using surface gradient upwind method

Cited by 46 publications

References 29 publications

Efficient numerical computation and experimental study of temporally long equilibrium scour development around abutment

Efficient numerical computation and experimental study of temporally long equilibrium scour development around abutment

Shallow sediment transport flow computation using time-varying sediment adaptation length

A finite element/volume method model of the depth‐averaged horizontally 2D shallow water equations

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