Unstructured Grid Finite-Volume Algorithm for Shallow-Water Flow and Scalar Transport with Wetting and Drying

Begnudelli, Lorenzo; Sanders, Brett F.

doi:10.1061/(asce)0733-9429(2006)132:4(371)

Cited by 192 publications

(141 citation statements)

References 19 publications

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“…The comparison of numerical and analytical solutions shows excellent agreement; however, discharge for flow with shock in Figure 8 shows discrepancy with the analytical solution at x = 12 m, which is where shock is generated. This disagreement was also observed previously in [20,28,38]. We measured convergence of solution for transcritical flow with a shock by using global relative error:…”

Section: Subcritical Flowsupporting

confidence: 65%

“…Unphysical velocities can be satisfactorily avoided by employing a positivity preserving the hydrostatic reconstruction method to modify flow variables at the interface between two adjacent cells and setting a threshold limit on water depth [23,[26][27][28]. We set a threshold of 10 −5 m in this study to prevent occurrence of negative water depths; a cell is considered dry if water depth in a cell is less than threshold limit which sets the velocity at interfaces of a cell to zero.…”

Section: Introductionmentioning

confidence: 99%

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Novel Slope Source Term Treatment for Preservation of Quiescent Steady States in Shallow Water Flows

Rehman

Cho

2016

Water

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This paper proposes a robust method for modeling shallow-water flows and near shore tsunami propagation, applicable for both simple and complex geometries with uneven beds. The novel aspect of the model includes the introduction of a new method for slope source terms treatment to preserve quiescent equilibrium over uneven topographies, applicable to both structured and unstructured mesh systems with equal accuracy. Our model is based on the Godunov-type finite volume numerical approximation. Second-order spatial and temporal accuracy is achieved through high resolution gradient reconstruction and the predictor-corrector method, respectively. The approximate Riemann solver of Harten, Lax, and van Leer with contact wave restoration (HLLC) is used to compute fluxes. Comparisons of the model's results with analytical, experimental, and published numerical solutions show that the proposed method is capable of accurately predicting experimental and real-time tsunami propagation/inundation, and dam-break flows over varying topographies.

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Section: Subcritical Flowsupporting

confidence: 65%

Section: Introductionmentioning

confidence: 99%

Novel Slope Source Term Treatment for Preservation of Quiescent Steady States in Shallow Water Flows

Rehman

Cho

2016

Water

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“…In addition to a dambreak flow over a dry bed without considering the diffusion effect on material concentration [5][6][7], the behavior of a dambreak flow over a wet bed involving the diffusion coefficient D u of 100 m 2 /s is also conducted herein [4].…”

Section: A Unit-step Tracer In a 1d Dambreak Flowmentioning

confidence: 99%

SPH Simulations of Solute Transport in Flows with Steep Velocity and Concentration Gradients

Chang

2017

Water

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Abstract:In this study, a meshless particle method, smoothed particle hydrodynamics (SPH), is adopted to solve the shallow water equations (SWEs) and the advection diffusion equations (ADEs) for simulating solute transport processes under 1D/2D conditions with steep gradients. A new SPH-SWEs-ADEs model is herein developed to focus on the numerical performance of solute transport in flows with steep velocity and concentration gradients, since the traditional mesh-based methods have numerical difficulties on solving such steep velocity/concentration gradient flows. The present model is validated by six benchmark study cases, including three steep concentration gradient cases and three coupled steep concentration/velocity gradient cases. The comparison between the simulated results and the exact solutions for the former three cases shows that complete mass concentration conservation in pure advection-dominated flows is preserved. The numerical oscillation in concentration and the negative concentration resulted from the discretization of the advection term of ADEs can be totally avoided. The other three cases confirm that this model can also well capture coupled steep gradients of velocities and concentrations. It is demonstrated that the presented solver is an effective and reliable tool to investigate solute transports in complex flows incorporating steep velocity gradients.

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“…However partially wetted cells i.e. cells without enough water to submerge all corners of the cell, the average depth are badly represented by depth at the centroid (Begnudelli and Sanders, 2006). Especially for a cell having very small water depth, the incidence of dry/wet condition will be very high and would frequently lead to model instability.…”

Section: Process Representation For Wetting/drying Cellsmentioning

confidence: 99%

A simple 2-D inundation model for incorporating flood damage in urban drainage planning

Pathirana

Tsegaye

Gersonius

et al. 2011

Hydrol. Earth Syst. Sci.

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Abstract. An urban inundation model was developed and coupled with 1-D drainage network model (EPA-SWMM5). The objective was to achieve a 1-D/2-D coupled model that is simple and fast enough to be consistently used in planning stages of urban drainage projects. The 2-D inundation model is based on a non-standard simplification of the shallow water equation, lays between diffusion-wave and full dynamic models. Simplifications were made in the process representation and numerical solving mechanisms and a depth scaled Manning coefficient was introduced to achieve stability in the cell wetting-drying process. The 2-D model is coupled with SWMM for simulation of both network flow and surcharge induced inundation. The coupling is archived by mass transfer from the network system to the 2-D system. A damage calculation block is integrated within the model code for assessing flood damage costs in optimal planning of urban drainage networks. The model is stable in dealing with complex flow conditions, and cell wetting/drying processes, as demonstrated by a number of idealised experiments. The model application is demonstrated by applying to a case study in Brazil.

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Unstructured Grid Finite-Volume Algorithm for Shallow-Water Flow and Scalar Transport with Wetting and Drying

Cited by 192 publications

References 19 publications

Novel Slope Source Term Treatment for Preservation of Quiescent Steady States in Shallow Water Flows

Novel Slope Source Term Treatment for Preservation of Quiescent Steady States in Shallow Water Flows

SPH Simulations of Solute Transport in Flows with Steep Velocity and Concentration Gradients

A simple 2-D inundation model for incorporating flood damage in urban drainage planning

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