Journal ArticleDOI
Simulation of one-dimensional dam-break flows
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TLDR
In this paper, Gabutti and Beam and Warming (BW) finite difference schemes are used for the analysis of free-surface flows resulting from the breaking of a dam.Abstract:
Two new finite-difference schemes - Gabutti, and Beam and Warming - are introduced and compared for the analysis of unsteady free-surface flows resulting from the breaking of a dam. These schemes split the fluxvector into positive and negative parts, each of which corresponds to the direction of a characteristic, thereby allowing use of proper finite differences for the space derivatives. Central finite differences are used for subcritical flow and upwind differences are used for supercritical flow. The details of these schemes are presented and the computed results are compared with the analytical solution to demonstrate their validity. Because of their simplicity, these schemes are attractive for solving the dam-break problem, especially when supercritical flow is present.read more
Citations
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Journal ArticleDOI
Riemann wave description of erosional dam-break flows
Luigi Fraccarollo,Hervé Capart +1 more
TL;DR: In this article, the authors examined the sudden erosional flow initiated by the release of a dam-break wave over a loose sediment bed and formulated extended shallow-water equations to describe the development of the surge.
Journal ArticleDOI
Explicit Methods for 2‐D Transient Free Surface Flows
TL;DR: MacCormack and Gabutti as mentioned in this paper introduced explicit finite-difference schemes to integrate the equations describing two-dimensional, unsteady gradually varied flows, which allow sharp discontinuous initial conditions, and do not require isolation of the bores.
Journal ArticleDOI
Approximate Riemann solutions of the shallow water equations
TL;DR: In this article, a finite difference scheme based on flux difference splitting is presented for the solution of the onedimensional shallow water equations of ideal fluid flow, analogous to a linearised problem.
Journal ArticleDOI
A Godunov method for the computation of erosional shallow water transients
TL;DR: In this article, a finite volume numerical solver is constructed, then extended to second-order accuracy using Strang splitting and MUSCL extrapolation, and lateralisation of the momentum flux is adopted to handle the non-conservative product associated with bottom slope.
Journal ArticleDOI
Numerical and experimental water transients in sewer pipes
Hervé Capart,X. Sillen,Yves Zech +2 more
TL;DR: In this paper, the Pavia Flux Predictor scheme (P.F.P) was used to describe hydraulic jumps and bores over a few grid points, and experiments were carried out for a steep slope circular pipe.
References
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Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes
TL;DR: In this paper, a new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in arbitrary geometric domains.
Journal ArticleDOI
Difference Methods for Initial-Value Problems.
Difference methods for initial-value problems
Robert D. Richtmyer,K. W. Morton +1 more
TL;DR: In this article, differentielles and stabilite were used for differentiable transport in the context of transfert de chaleur and ondes Reference Record created on 2005-11-18, modified on 2016-08-08
An implicit finite-difference algorithm for hyperbolic systems in conservation-law form. [application to Eulerian gasdynamic equations
R. M. Beam,R. F. Warming +1 more
TL;DR: In this article, an implicit finite-difference scheme is developed for the efficient numerical solution of nonlinear hyperbolic systems in conservation law form, which is second-order time-accurate, noniterative, and in a spatially factored form.