Well-Balanced Scheme between Flux and Source Terms for Computation of Shallow-Water Equations over Irregular Bathymetry

Kim, Dae Hong; Cho, Yong-Sik; Kim, Hyung Jun

doi:10.1061/(asce)0733-9399(2008)134:4(277)

Cited by 39 publications

(23 citation statements)

References 13 publications

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“…This test problem is widely used to verify well-balanced property of a numerical scheme towards moving steady state solution [7,8,25]. The moving steady-state water equilibrium is given by: …”

Section: Flow Over a Humpmentioning

confidence: 99%

“…For SGM [20] and RSGM [7] methods, convergence is achieved after 16,000 and 15,600 iterations, respectively. between numerical and exact solutions of water depth than for discharge which is due to discrepancy between exact and numerical discharge immediately downstream of the hump, however, the overall agreement between computed and exact solution is satisfactory.…”

Section: Subcritical Flowmentioning

confidence: 99%

“…With appropriate numerical techniques, SWEs can model complex flows that involve sharp discontinuities and shocks. The most challenging issues in modeling shallow flows involve maintaining second-order accuracy, satisfying well-balanced condition, and avoiding numerical instabilities at wet-dry fronts [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

“…Some of the popular methods of establishing second-order accuracy are Monotonic Upwind Scheme for Conservation Laws (MUSCL) scheme [1,[7][8][9], the Weighted Essentially Non-Oscillatory (WENO) scheme [10][11][12], and a high-resolution reconstruction procedure developed by [13] which has been widely employed for shallow water flows [5,14,15]. Reconstruction by MUSCL scheme may result in negative water depths at the interface which consequently give unphysical high velocities because of discharge divided by small water depths [16].…”

Section: Introductionmentioning

confidence: 99%

“…It is worth mentioning some of the classical well-balanced numerical approaches. Popular approaches include the upwind discretization of slope terms [18,19], the surface water gradient (SGM) methods in which the water surface level is used as a conservative variable instead of water depth [7,20,21]; the hydrostatic reconstruction method proposed by [22] is another popular method among researchers [16,[23][24][25]. 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.…”

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: Flow Over a Humpmentioning

confidence: 99%

Section: Subcritical Flowmentioning

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 simple and efficient unstructured finite volume scheme for solving the shallow water equations in overland flow applications

Cea

Castellet

2015

Water Resources Research

174

120

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This paper presents the decoupled hydrological discretization (DHD) scheme for solving the shallow water equations in hydrological applications involving surface runoff in rural and urban basins. The name of the scheme is motivated by the fact that the three equations which form the two-dimensional shallow water system are discretized independently from each other and thus, the numerical scheme is decoupled in a mathematical sense. Its main advantages compared to other classic finite volume schemes for the shallow water equations are its simplicity to code and the lower computational cost per time step. The validation of the scheme is presented in five test cases involving overland flow and rainfall-runoff transformation over topographies of different complexity. The scheme is compared to the finite volume scheme of Roe (1986), to the simple inertia formulation, and to the diffusive wave model. The test cases show that the DHD scheme is able to compute subcritical and supercritical flows in rural and urban environments, and that in overland flow applications it gives similar results to the second-order scheme of Roe with a lower computational cost. The results obtained with the simple inertia and diffusive wave models are very similar to those obtained with the DHD scheme in rural basins in which the bed friction and topography dominate the flow hydrodynamics but they deteriorate in typical urban configurations in which the presence of supercritical flow conditions and small-scale patterns boost the relevance of the inertial terms in the momentum equations.

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Contradiction between the C‐property and mass conservation in adaptive grid based shallow flow models: cause and solution

Liang

Hou

Xia

2015

Numerical Methods in Fluids

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SummaryWhen performing shallow flow simulations on adaptive grids, the C‐property (i.e. conservation property) and the mass conservation may not be simultaneously preserved, that is, either C‐property or mass conservation is likely to be violated following grid refining or coarsening. The cause of such a contradiction is analyzed in detail in this work, which essentially links to the reconstruction of bed and flow information in those newly created cells during grid adaptation. An effective approach is subsequently proposed to resolve the contradiction by locally modifying the bed elevation in certain problematic cells when reconstructing flow information using linear interpolation as part of the grid adaptation procedure. Copyright © 2015 John Wiley & Sons, Ltd.

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Well-Balanced Scheme between Flux and Source Terms for Computation of Shallow-Water Equations over Irregular Bathymetry

Cited by 39 publications

References 13 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 simple and efficient unstructured finite volume scheme for solving the shallow water equations in overland flow applications

Contradiction between the C‐property and mass conservation in adaptive grid based shallow flow models: cause and solution

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