Numerical solution of the two-dimensional unsteady dam break

Zoppou, Christopher; Roberts, Stephen

doi:10.1016/s0307-904x(99)00056-6

Cited by 91 publications

(59 citation statements)

References 20 publications

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“…We observe a bore travelling downstream and a rarefaction wave travelling upstream. The results are, in general, similar to results presented in the literature [2,24,23] with the exception of the Gibbs oscillations inevitably produced by a high-order method without limiting. The solution is initially improved by the increase of polynomial order.…”

Section: Dam-breaksupporting

confidence: 89%

A triangular spectral/hp discontinuous Galerkin method for modelling 2D shallow water equations

Eskilsson

Sherwin

2004

Numerical Methods in Fluids

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SUMMARYWe present a spectral/hp element discontinuous Galerkin model for simulating shallow water flows on unstructured triangular meshes. The model uses an orthogonal modal expansion basis of arbitrary order for the spatial discretisation and a third-order Runge-Kutta scheme to advance in time. The local elements are coupled together by numerical fluxes, evaluated using the HLLC Riemann solver. We apply the model to test cases involving smooth flows and demonstrate the exponentially fast convergence with regard to polynomial order. We also illustrate that even for results of "engineering

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Section: Dam-breaksupporting

confidence: 89%

A triangular spectral/hp discontinuous Galerkin method for modelling 2D shallow water equations

Eskilsson

Sherwin

2004

Numerical Methods in Fluids

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“…Specifically, it is solved by total variation diminishing version of the weight averaged flux method, with extended Harten-Leer-Lax Riemann solver [40,54]. As explained in the references above, the shoreline is captured by solving exact Riemann problem on the dry/wet interface.…”

Section: Surface Wave Simulatormentioning

confidence: 99%

Liquefaction potential of coastal slopes induced by solitary waves

et al. 2009

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Tsunami runup and drawdown can cause liquefaction failure of coastal fine sand slopes due to the generation of high excess pore pressure and the reduction of the effective over burden pressure during the drawdown. The region immediately seaward of the initial shoreline is the most susceptible to tsunami-induced liquefaction failure because the water level drops significantly below the still water level during the set down phase of the drawdown. The objective of this work is to develop and validate a numerical model to assess the potential for tsunamiinduced liquefaction failure of coastal sandy slopes. The transient pressure distribution acting on the slope due to wave runup and drawdown is computed by solving for the hybrid Boussinesq-nonlinear shallow water equations using a finite volume method. The subsurface pore water pressure and deformation fields are solved simultaneously using a finite element method. Two different soil constitutive models have been examined: a linear elastic model and a non-associative Mohr-Coulomb model. The numerical methods are validated by comparing the results with analytical models, and with experimental measurements from a large-scale laboratory study of breaking solitary waves over a planar fine sand beach. Good comparisons were observed from both the analytical and experimental validation studies. Numerical case studies are shown for a full-scale simulation of a 10-m solitary wave over a 1:15 and 1:5 sloped fine sand beach. The results show that the soil near the bed surface, particularly along the seepage face, is at risk to liquefaction failure. The depth of the seepage face increases and the width of the seepage face decreases with increasing bed slope. The rate of bed surface loading and unloading due to wave runup and drawdown, respectively, also increases with increasing bed slope. Consequently, the case with the steeper slope is more susceptible to liquefaction failure due to the higher hydraulic gradient. The analysis also suggests that the results are strongly influenced by the soil permeability and relative compressibility between the pore fluid and solid skeleton, and that a coupled solid/fluid formulation is needed for the soil solver. Finally, the results show the drawdown pore pressure response is strongly influenced by nonlinear material behavior for the full-scale simulation.

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“…However, in order to avoid the singularity of the numerical solution at the intersection point, they had to pre-wet the bed in front of the dam by an artificial thin fluid layer. Several numerical studies performed during the past few years were based on the solution of nonlinear shallow-water equations using different methods such as the finite-volume method, the finite-difference method and so on (see [6][7][8][9][10][11]). There are very few asymptotic analyses of the dam-break problem.…”

mentioning

confidence: 99%

The initial stage of dam-break flow

Korobkin

Yılmaz

2008

J Eng Math

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The liquid flow and the free surface shape during the initial stage of dam breaking are investigated. The method of matched asymptotic expansions is used to derive the leading-order uniform solution of the classical dam-break problem. The asymptotic analysis is performed with respect to a small parameter which characterizes the short duration of the stage under consideration. The second-order outer solution is obtained in the main flow region. This solution is not valid in a small vicinity of the intersection point between the initially vertical free surface and the horizontal rigid bottom. The dimension of this vicinity is estimated with the help of a local analysis of the outer solution close to the intersection point. Stretched local coordinates are used in this vicinity to resolve the flow singularity and to derive the leading-order inner solution, which describes the formation of the jet flow along the bottom. It is shown that the inner solution is self-similar and the corresponding boundary-value problem can be reduced to the well-known Cauchy-Poisson problem for water waves generated by a given pressure distribution along the free surface. An analysis of the inner solution reveals the complex shape of the jet head, which would be difficult to simulate numerically. The asymptotic solution obtained is expected to be helpful in the analysis of developed gravity-driven flows.

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Numerical solution of the two-dimensional unsteady dam break

Cited by 91 publications

References 20 publications

A triangular spectral/hp discontinuous Galerkin method for modelling 2D shallow water equations

A triangular spectral/hp discontinuous Galerkin method for modelling 2D shallow water equations

Liquefaction potential of coastal slopes induced by solitary waves

The initial stage of dam-break flow

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