Locally Limited and Fully Conserved RKDG2 Shallow Water Solutions with Wetting and Drying

Kesserwani, Georges; Liang, Qiuhua

doi:10.1007/s10915-011-9476-4

Cited by 42 publications

(36 citation statements)

References 52 publications

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“…In the first step of the calculation, the upper ordinary differential equation in (23) is approximated by an implicit method as described in [21]:…”

Section: Modelling and Simulation In Engineeringmentioning

confidence: 99%

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Numerical Simulation of Dam Break Flows Using a Radial Basis Function Meshless Method with Artificial Viscosity

Chaabelasri

2018

Modelling and Simulation in Engineering

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A simple radial basis function (RBF) meshless method is used to solve the two-dimensional shallow water equations (SWEs) for simulation of dam break flows over irregular, frictional topography involving wetting and drying. At first, we construct the RBF interpolation corresponding to space derivative operators. Next, we obtain numerical schemes to solve the SWEs, by using the gradient of the interpolant to approximate the spatial derivative of the differential equation and a third-order explicit Runge-Kutta scheme to approximate the temporal derivative of the differential equation. For the problems involving shock or discontinuity solutions, we use an artificial viscosity for shock capturing. en, we apply our scheme for several theoretical twodimensional numerical experiments involving dam break flows over nonuniform beds and moving wet-dry fronts over irregular bed topography. Promising results are obtained.

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“…In the first step of the calculation, the upper ordinary differential equation in (23) is approximated by an implicit method as described in [21]:…”

Section: Modelling and Simulation In Engineeringmentioning

confidence: 99%

“…e friction term is included in the momentum equations and discretized by a splitting implicit scheme [21]. A third-order Runge-Kutta algorithm is used for time integration [22].…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Dam Break Flows Using a Radial Basis Function Meshless Method with Artificial Viscosity

Chaabelasri

2018

Modelling and Simulation in Engineering

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“…This test case has been employed for model testing as it simultaneously includes propagating bores and reflection waves, wetting and drying, surface curvatures, and steady-state equilibrium. 25 As shown in Figure 5, the channel is 7 m long and involves two trapezoidal humps (hump A and hump B). The dam is built along the central line on the top of hump A. Upstream of the dam, the initially stationary water level is set to 0.45 m, and the downstream area is initially dry.…”

Section: Test 3: Dam-break Flow Over Two Trapezoidal Humpsmentioning

confidence: 99%

Two-dimensional shallow water flow modeling based on an improved unstructured finite volume algorithm

Song

Zhou

et al. 2015

Advances in Mechanical Engineering

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An improved finite volume algorithm is proposed for modeling the free surface flows. The effects of variable reconstruction and treatments for partially wetted cells on numerical oscillations are demonstrated through a complex field-scale simulation. Results show that the combination of a vertex-based slope limiting approach and an updating strategy that the continuity and momentum equations should be simultaneously updated for partially wetted cells is essential to prevent unphysical oscillations. In this situation, the bed slope terms in wetted cells are exactly discretized, whereas the divergence-form-based approach is adopted for partially wetted cells. This new hybrid method provides an alternative way that precisely preserves the well-balanced property. A practical application of realistic dam-break flood propagation is presented. It is found that the model is free of numerical oscillation and can accurately predict dam-break flows over complicated topography with wetting and drying.

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“…Certainly, the reliability of a fully-coupled morphodynamic numerical model is further 47 dependent on its further ability to handle wet/dry fronts along with the complex source terms. These are 48 desirable features to possess within the design of a second-order accurate hydro-morphodynamic 49 numerical model, which is the purpose of this work on the subject of an extension to a well-established 50 RKDG2 (second-order Runge-Kutta [RK] DG) hydrodynamic solver (Kesserwani and Liang 2012b). 51…”

Section: Toro and 35mentioning

confidence: 99%

Fully Coupled Discontinuous Galerkin Modeling of Dam-Break Flows over Movable Bed with Sediment Transport

2014

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Locally Limited and Fully Conserved RKDG2 Shallow Water Solutions with Wetting and Drying

Abstract: This work extends a well-balanced second-order Runge-Kutta discontinuous Galerkin

Cited by 42 publications

References 52 publications

Numerical Simulation of Dam Break Flows Using a Radial Basis Function Meshless Method with Artificial Viscosity

Numerical Simulation of Dam Break Flows Using a Radial Basis Function Meshless Method with Artificial Viscosity

Two-dimensional shallow water flow modeling based on an improved unstructured finite volume algorithm

Fully Coupled Discontinuous Galerkin Modeling of Dam-Break Flows over Movable Bed with Sediment Transport

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