A conservative extension of the method of characteristics for 1-D shallow flows

SUMMARYThis paper comprises an implementation of a fourth-order Runge-Kutta discontinuous Galerkin (RKDG4) scheme for computing the open-channel flow equations. The main features of the proposed methodology are simplicity and easiness in the implementation, which may be of possible interest to water resources numerical modellers. A version of the RKDG4 is blended with the Roe Riemann solver, an adaptive high-order slope limiting procedure, and high-order source terms approximations. A comparison of the performance of the proposed method with lower-order RKDG models is performed showing a benefit of considering the RKDG4 model. The scheme is applied to computerize the Saint Venant system by considering benchmark tests that have exact solutions. Finally, numerical results are illustrated discussing the performance of the proposed high-order model.

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“…Recently developed research codes [8,9,11,12,14,15,17,56] are based on the conservative formulation of this set of hyperbolic PDE, namely…”

Section: Open-channel Flow Equationsmentioning

confidence: 99%

A practical implementation of high‐order RKDG models for the 1D open‐channel flow equations

Kesserwani

Mosé²,

Vázquez³

et al. 2008

Numerical Methods in Fluids

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“…Dam break on a flat bed. The dam-break problem is the most common test to evaluate the performance of shock capturing schemes in shallow flows, such as [15]. The bottom is flat b(x) = 0 and the initial conditions are taken as:…”

Section: Numerical Resultsmentioning

confidence: 99%

A Numerical Study for the Performance of the WENO Schemes Based on Different Numerical Fluxes for the Shallow Water Equations

Lu¹,

Qiu²,

Wang³

2010

JCM

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In this paper we investigate the performance of the weighted essential non-oscillatory (WENO) methods based on different numerical fluxes, with the objective of obtaining better performance for the shallow water equations by choosing suitable numerical fluxes. We consider six numerical fluxes, i.e., Lax-Friedrichs, local Lax-Friedrichs, Engquist-Osher, Harten-Lax-van Leer, HLLC and the first-order centered fluxes, with the WENO finite volume method and TVD Runge-Kutta time discretization for the shallow water equations. The detailed numerical study is performed for both one-dimensional and two-dimensional shallow water equations by addressing the issues of CPU cost, accuracy, non-oscillatory property, and resolution of discontinuities.Mathematics subject classification: 65M60, 65M99, 35L65.

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“…It is based on non-conservative equations; hence, it cannot be used directly for solving discontinuous and transcritical flows [9]. On the other hand, this form provides insight into shallow water wave motion, which is not evident in the other forms.…”

Section: Externalmentioning

confidence: 99%

“…Crossely and Wright [4] applied two local time stepping (LTS) strategies to simulate the one-dimensional unsteady water flows. Mohammadian et al [9] carried forward an extension to the non-conservative method of characteristics (MOC). By using a proper interpolation function, the MOC is rendered conservative and can handle challenging tests for the one-dimensional open-channel flow (dam-break type, transcritical flows).…”

Section: Numerical Model Selectionmentioning

confidence: 99%

One‐dimensional simulation of supercritical flow at a confluence by means of a nonlinear junction model applied with the RKDG2 method

Kesserwani

Ghostine

Vázquez³

et al. 2007

Numerical Methods in Fluids

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International audienceWe investigate the one-dimensional computation of supercritical open-channel flows at a combining junction. In such situations, the network system is composed of channel segments arranged in a branching configuration, with individual channel segments connected at a junction. Therefore, two important issues have to be addressed: (a) the numerical solution in branches, and (b) the internal boundary conditions treatment at the junction. Going from the advantageous literature supports of RKDG methods to a particular investigation for a supercritical benchmark, the second-order Runge-Kutta discontinuous Galerkin (RKDG2) scheme is selected to compute the water flow in branches. For the internal boundary handling, we propose a new approach by incorporating the nonlinear model derived from the conservation of the momentum through the junction. The nonlinear junction model was evaluated against available experiments and then applied to compute the junction internal boundary treatment for steady and unsteady flow applications. Finally, a combining flow problem is defined and simulated by the proposed framework and results are illustrated for many choices of junction angles. Copyright © 2007 John Wiley & Sons, Ltd

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A conservative extension of the method of characteristics for 1-D shallow flows

Cited by 17 publications

References 18 publications

A practical implementation of high‐order RKDG models for the 1D open‐channel flow equations

A practical implementation of high‐order RKDG models for the 1D open‐channel flow equations

A Numerical Study for the Performance of the WENO Schemes Based on Different Numerical Fluxes for the Shallow Water Equations

One‐dimensional simulation of supercritical flow at a confluence by means of a nonlinear junction model applied with the RKDG2 method

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