A 2D well-balanced shallow flow model for unstructured grids with novel slope source term treatment

Hou, Jingming; Liang, Qiuhua; Simons, Franz; Hinkelmann, Reinhard

doi:10.1016/j.advwatres.2012.08.003

Cited by 118 publications

(89 citation statements)

References 74 publications

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“…The hydrostatic reconstruction method is applicable for both structured and unstructured meshes but for second-order schemes additional source term treatments are required [2,22]. Hou et al [26] proposed an improvement to the existing slope source term treatment methods by offering a scheme that could be extended to high-order accuracies without complication. Their method was based on the splitting of a cell into sub-cells and approximating the flux by adding fluxes through the sub-cells.…”

Section: Introductionmentioning

confidence: 99%

“…Their method was based on the splitting of a cell into sub-cells and approximating the flux by adding fluxes through the sub-cells. Hou et al [16] further improved the scheme proposed in [26] through local modification of the bed elevation in slope source terms and through a better approximation of water depths at the interface by hydrostatic reconstruction.…”

Section: Introductionmentioning

confidence: 99%

“…The upwind method performs well for first-order schemes, but needs additional source term treatment for higher-order schemes, rendering this method both complicated and expensive. The surface gradient method is typically proposed for structured grids and does not offer the flexibility of being applicable to all mesh types [26]. The hydrostatic reconstruction method is applicable for both structured and unstructured meshes but for second-order schemes additional source term treatments are required [2,22].…”

Section: Introductionmentioning

confidence: 99%

“…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%

“…Therefore, in this study, we propose a novel slope source term treatment method which possesses all the features of a robust numerical scheme without any compromise on accuracy, simplicity and computational efficiency. We convert the slope terms into fluxes at the interface as previously done in [16,26], but with a different mathematical formulation to average water depth in convective flux and slope source terms. Unlike [16] where the scheme needs to switch to first-order accuracy at wet-dry interfaces to avoid numerical instabilities, the proposed method, paired with the multidimensional reconstruction method, is able to maintain second-order accuracy throughout the domain including at the wet-dry interfaces.…”

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: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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A faster numerical scheme for a coupled system modeling soil erosion and sediment transport

Cordier

Lucas

2015

Water Resources Research

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Overland flow and soil erosion play an essential role in water quality and soil degradation.Such processes, involving the interactions between water flow and the bed sediment, are classically described by a well-established system coupling the shallow water equations and the Hairsine-Rose model. Numerical approximation of this coupled system requires advanced methods to preserve some important physical and mathematical properties; in particular, the steady states and the positivity of both water depth and sediment concentration. Recently, finite volume schemes based on Roe's solver have been proposed by Heng et al. (2009) and Kim et al. (2013) for one and two-dimensional problems. In their approach, an additional and artificial restriction on the time step is required to guarantee the positivity of sediment concentration. This artificial condition can lead the computation to be costly when dealing with very shallow flow and wet/dry fronts. The main result of this paper is to propose a new and faster scheme for which only the CFL condition of the shallow water equations is sufficient to preserve the positivity of sediment concentration. In addition, the numerical procedure of the erosion part can be used with any well-balanced and positivity preserving scheme of the shallow water equations. The proposed method is tested on classical benchmarks and also on a realistic configuration.

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An efficient and stable hydrodynamic model with novel source term discretization schemes for overland flow and flood simulations

Xia

Liang

Ming

et al. 2017

Water Resources Research

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144

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Numerical models solving the full 2‐D shallow water equations (SWEs) have been increasingly used to simulate overland flows and better understand the transient flow dynamics of flash floods in a catchment. However, there still exist key challenges that have not yet been resolved for the development of fully dynamic overland flow models, related to (1) the difficulty of maintaining numerical stability and accuracy in the limit of disappearing water depth and (2) inaccurate estimation of velocities and discharges on slopes as a result of strong nonlinearity of friction terms. This paper aims to tackle these key research challenges and present a new numerical scheme for accurately and efficiently modeling large‐scale transient overland flows over complex terrains. The proposed scheme features a novel surface reconstruction method (SRM) to correctly compute slope source terms and maintain numerical stability at small water depth, and a new implicit discretization method to handle the highly nonlinear friction terms. The resulting shallow water overland flow model is first validated against analytical and experimental test cases and then applied to simulate a hypothetic rainfall event in the 42 km2 Haltwhistle Burn, UK.

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A 2D well-balanced shallow flow model for unstructured grids with novel slope source term treatment

Cited by 118 publications

References 74 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

A faster numerical scheme for a coupled system modeling soil erosion and sediment transport

An efficient and stable hydrodynamic model with novel source term discretization schemes for overland flow and flood simulations

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