Zero mass error using unsteady wetting–drying conditions in shallow flows over dry irregular topography

Brufau, P.; García‐Navarro, P.; Vázquez-Cendón, M. Elena

doi:10.1002/fld.729

Cited by 193 publications

(153 citation statements)

References 22 publications

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“…Propagation of flow at a wet/dry interface with a downward gradient can be handled straightforwardly by setting a tolerance value for water depth and solving it as the Riemann problem. However, flooding and drying process over an adverse slope can cause spontaneous movement of water to adjacent dry cells and damage the balance between flux and source terms (Brufau et al, 2002(Brufau et al, , 2004Cea et al, 2006).…”

Section: Wet-dry Analysismentioning

confidence: 99%

“…For the computation of the bed slope term, S b , in Eqs. (4) and (5), this study utilizes the source term discretization method proposed by Brufau et al (2004), which gives To have more accurate solutions, the second-order schemes can be utilized. Different from the first-order scheme using directly the values at cell centers, the conserved variables are first reconstructed at the left and right sides of cell edges using the cell gradient method.…”

Section: Space Schemementioning

confidence: 99%

“…The method using the upwind scheme to the source terms and the eigenvector projection has also been applied to solve the equilibrium condition problem (Bermudez and Vazquez, 1994;Brufau et al, 2004;Hubbard and Garcia-Navarro;2000). This method allows the total slope terms to be calculated by summing the bed slope source terms at each edge in terms of the projected eigenvectors.…”

Section: Introductionmentioning

confidence: 99%

“…Their approach adopted the assumption that the water surface level is constant and the gradient in surface level is zero at quiescent flow conditions. Other methods have also been employed to resolve this issue (Audusse and Bristeau, 2005;Bermudez and Vazquez, 1994;Bradford and Sanders, 2002;Brufau et al, 2004;Rogers et al, 2003;Valiani and Begnudelli, 2006).…”

Section: Introductionmentioning

confidence: 99%

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An object-oriented overland flow solver for watershed flood inundation predictions: case study of Ulus basin, Turkey

Turan

Wang

2014

Journal of Hydrology and Hydromechanics

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This paper presents an object-oriented two-dimensional (2-D) overland flow model and its application in simulating flood flows over Ulus basin, located in the north of Turkey adjacent to the Black Sea. A new coding implementation according to the class environment created in object oriented C++ programming language is carried out in structuring and building the solver. The model is based on the Godunov type finite volume scheme on unstructured triangular meshes. A mass balance preserving wet/dry boundary solution algorithm is integrated in the numerical scheme to satisfy the positive-depth condition and minimize the numerical instability when treating the propagation of wave front in regions of dry bed. The balance between bed slope and flux terms is also preserved for still water conditions on irregular topography. The 2-D solver is verified by simulating selected dam break cases, where good agreement with measured data is achieved. For the simulation of flood flows in the Ulus basin, in general, the simulated outflow hydrograph is found to compare well with the recorded data. A selected inundation map that is extracted from the model results is also presented to show the water surface level in the Floodplain.

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Section: Wet-dry Analysismentioning

confidence: 99%

Section: Space Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An object-oriented overland flow solver for watershed flood inundation predictions: case study of Ulus basin, Turkey

Turan

Wang

2014

Journal of Hydrology and Hydromechanics

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“…First order FV schemes are widely found in the literature [2,3,4,5,6,7,8]. The conceptual simplicity of first order FV schemes and its rather straightforward implementation and ease for parallelization have made it very popular.…”

Section: Introductionmentioning

confidence: 99%

Multiwavelet-based grid adaptation with discontinuous Galerkin schemes for shallow water equations

Gerhard

Caviedes‐Voullième

Müller

et al. 2015

Journal of Computational Physics

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We provide an adaptive strategy for solving shallow water equations with dynamic grid adaptation including a sparse representation of the bottom topography. A challenge in computing approximate solutions to the shallow water equations including wetting and drying is to achieve the positivity of the water height and the well-balancing of the approximate solution. A key property of our adaptive strategy is that it guarantees that these properties are preserved during the refinement and coarsening steps in the adaptation process.The underlying idea of our adaptive strategy is to perform a multiresolution analysis using multiwavelets on a hierarchy of nested grids. This provides difference information between successive refinement levels that may become negligibly small in regions where the solution is locally smooth. Applying hard thresholding the data are highly compressed and local grid adaptation is triggered by the remaining significant coefficients. Furthermore we use the multiresolution analysis of the underlying data as an additional indicator whether the limiter has to be applied on a cell or not. By this the number of cells where the limiter is applied is reduced without spoiling the accuracy of the solution.By means of well-known 1D and 2D benchmark problems, we verify that multiwavelet-based grid adaptation can significantly reduce the computational cost by sparsening the computational grids, while retaining accuracy and keeping well-balancing and positivity.

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Finite volume simulation of waves formed by sliding masses

Delis

Καζολέα

2011

Int. J. Numer. Meth. Biomed. Engng.

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SUMMARYWe numerically study a relatively simple two-dimensional (2D) model for landslide-generated nonlinear surface water waves. The landslides are modeled as rigid and impervious bodies translating on a flat or an inclined bottom. The water motion is assumed to be properly modeled by the 2D nonlinear system of shallow water equations. The resulting 2D system is numerically solved by means of a conservative well-balanced high-resolution finite volume upwind scheme esspecially adapted to treat advancing wet/dry fronts over irregular topography. Numerical results for 1D and 2D benchmark cases include comparisons with analytical or asymptotic solutions as well as comparisons with experimental data. The numerical investigation reveals that although the presented model has certain limitations, it appears to be able to model important aspects and the most significant characteristics of wave formation and propagation in their initial generation stage, namely, the waves moving toward the shore, the subsequent run-up and run-down, the waves propagating toward deep water, as well as the shape and arrival time of these waves.

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Zero mass error using unsteady wetting–drying conditions in shallow flows over dry irregular topography

Cited by 193 publications

References 22 publications

An object-oriented overland flow solver for watershed flood inundation predictions: case study of Ulus basin, Turkey

An object-oriented overland flow solver for watershed flood inundation predictions: case study of Ulus basin, Turkey

Multiwavelet-based grid adaptation with discontinuous Galerkin schemes for shallow water equations

Finite volume simulation of waves formed by sliding masses

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