Explicit Schemes for Dam-Break Simulations

Zoppou, Christopher; Roberts, Stephen

doi:10.1061/(asce)0733-9429(2003)129:1(11)

Cited by 104 publications

(59 citation statements)

References 70 publications

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“…(20). This graph agrees with the experimental result obtained by Nsom [9] who found the following scaling law in this regime In these experiments, the author performed dam-break tests using well characterized water-glucose syrup solutions. Generally, in the literature, theoretical studies focus on the long time solution also called asymptotic solution (e.g.…”

Section: Wave Front Positionsupporting

confidence: 90%

“…Then, an analytical solution is presented both for short time and long time behavior. Zoppou and Roberts [9] tested the performance of 20 explicit schemes used to solve the shallow water wave equations for simulating the dam-break problem. Comparing results from these schemes with analytical solutions to the dam-break problem with finite-water depth and dry bed downstream of the dam, they found that most of the numerical schemes produce reasonable results for subcritical flows.…”

Section: Introductionmentioning

confidence: 99%

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Equipment safety in renewable energies exploitation

Nson¹,

Bouchlaghem²

2011

REPQJ

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: This paper considers the dam-break problem in a horizontal smooth 1D channel, for the purpose of equipment safety in renewable energies exploitation. The fluid is water and it can be described by a Newtonian model, provided that the inertial effects be neglected versus the viscous ones in the momentum balance. Assuming the shallow water approximation, a non dimensional equation is built from the continuity and the Navier-Stokes equations in the limit of zero-inertia and it is solved analytically in two limits: short time and long time. These solutions are then combined into a single, universal model. Limitations of the model are examined by comparison to a converged finite difference numerical solution of the flow equation.

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Section: Wave Front Positionsupporting

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Equipment safety in renewable energies exploitation

Nson¹,

Bouchlaghem²

2011

REPQJ

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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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“…These tests, for which the Stoker (1957) solution is available, represent the benchmark of several second-order schemes considered by Zoppou and Roberts (2003) . The adopted spatial discretization ( x Δ =  20 m) is the same of Zoppou and Roberts (2003) and the time integration step t Δ  has been fixed equal to 1 s. The performance of the present numerical method has been assessed comparing the relative error L1-norm (Zoppou and Roberts, 2003) of the computed results. Both h  and u  variables have been considered and compared with the corresponding ones of the second-order models reported in Zoppou and Roberts (2003).…”

Section: Dam-break Testsmentioning

confidence: 99%

Inlet effects on roll-wave development in shallow turbulent open-channel flows

Campomaggiore

Cristo

Iervolino³

et al. 2016

Journal of Hydrology and Hydromechanics

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The present work investigates the effect of the flow profile induced by an inlet condition on the roll-wave evolution in turbulent clear-water flows. The study employs theoretical and numerical analyses. Firstly, the influence of the inlet condition on the spatial evolution of a single perturbation in a hypercritical flow is examined through the expansion near a wavefront analysis. The results show that an accelerated unperturbed profile reduces the disturbance spatial growth. A decelerated profile causes an increase. The effect of the flow profile on the spatial evolution of rollwave trains is then numerically investigated solving the Saint Venant equations with a second-order Runge-Kutta Total Variation Diminishing (TVD) Finite Volume scheme. The numerical simulations comply with the analytical results for the initial and transition phases of the roll-wave development. The unperturbed profile influences even the roll-waves statistical characteristics in the final stage, with a more evident effect in case of accelerated profiles. The influence of the flow profile should be therefore accounted for in the formulation of predictive criteria for roll-waves appearance based on the estimation of the disturbance spatial growth rate.

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Explicit Schemes for Dam-Break Simulations

Cited by 104 publications

References 70 publications

Equipment safety in renewable energies exploitation

Equipment safety in renewable energies exploitation

The initial stage of dam-break flow

Inlet effects on roll-wave development in shallow turbulent open-channel flows

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