A central WENO scheme for solving hyperbolic conservation laws on non-uniform meshes

Capdeville, G.

doi:10.1016/j.jcp.2007.11.029

Cited by 108 publications

(70 citation statements)

References 21 publications

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“…To satisfy the non-oscillation requirement, the third-order or fifth-order CWENO schemes [4][5] can be adopted to obtain the point values. For simplicity, only the fifth-order central WENO scheme is reviewed in the paper.…”

Section: Reconstruction Of the Point Valuesmentioning

confidence: 99%

“…However, the procedure produces significant numerical oscillations in the presence of discontinuity. The representative schemes of high-order and non-oscillatory schemes are the essentially nonoscillatory (ENO) scheme [1][2] , the weighted essentially non-oscillatory (WENO) scheme [3] , and the central (CWENO) scheme [4][5] . There are also other high-order schemes, such as the RKDG FEM [6] , shock-capturing difference schemes [7] , compact schemes [8] , the piecewise rational scheme (PRM) [9] , and the CIP/MM FVM schemes [10] .…”

Section: Introductionmentioning

confidence: 99%

“…To achieve high-order accuracy in time, a Simpson's quadrature rule is selected. Specially, the evaluation of point values at each sub-time stage along the characteristic curves is obtained by using CWENO reconstruction schemes [5] . The scheme combines with the high resolution of the characteristic method, and the high accuracy and non-oscillation of CWENO scheme.…”

Section: Introductionmentioning

confidence: 99%

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Characteristic-based finite volume scheme for 1D Euler equations

Guo

Ru-xun

2009

Appl. Math. Mech.-Engl. Ed.

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In this paper, a high-order finite-volume scheme is presented for the onedimensional scalar and inviscid Euler conservation laws. The Simpson , s quadrature rule is used to achieve high-order accuracy in time. To get the point value of the Simpson , s quadrature, the characteristic theory is used to obtain the positions of the grid points at each sub-time stage along the characteristic curves, and the third-order and fifthorder central weighted essentially non-oscillatory (CWENO) reconstruction is adopted to estimate the cell point values. Several standard one-dimensional examples are used to verify the high-order accuracy, convergence and capability of capturing shock.

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Section: Reconstruction Of the Point Valuesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Characteristic-based finite volume scheme for 1D Euler equations

Guo

Ru-xun

2009

Appl. Math. Mech.-Engl. Ed.

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“…Some of the popular methods of establishing second-order accuracy are Monotonic Upwind Scheme for Conservation Laws (MUSCL) scheme [1,[7][8][9], the Weighted Essentially Non-Oscillatory (WENO) scheme [10][11][12], and a high-resolution reconstruction procedure developed by [13] which has been widely employed for shallow water flows [5,14,15]. Reconstruction by MUSCL scheme may result in negative water depths at the interface which consequently give unphysical high velocities because of discharge divided by small water depths [16].…”

Section: Introductionmentioning

confidence: 99%

Novel Slope Source Term Treatment for Preservation of Quiescent Steady States in Shallow Water Flows

Rehman

Cho

2016

Water

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This paper proposes a robust method for modeling shallow-water flows and near shore tsunami propagation, applicable for both simple and complex geometries with uneven beds. The novel aspect of the model includes the introduction of a new method for slope source terms treatment to preserve quiescent equilibrium over uneven topographies, applicable to both structured and unstructured mesh systems with equal accuracy. Our model is based on the Godunov-type finite volume numerical approximation. Second-order spatial and temporal accuracy is achieved through high resolution gradient reconstruction and the predictor-corrector method, respectively. The approximate Riemann solver of Harten, Lax, and van Leer with contact wave restoration (HLLC) is used to compute fluxes. Comparisons of the model's results with analytical, experimental, and published numerical solutions show that the proposed method is capable of accurately predicting experimental and real-time tsunami propagation/inundation, and dam-break flows over varying topographies.

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“…Shi et al [35] present an efficient splitting technique to treat the negative weights without the necessity to remove them. Capdeville [36] proposes a new centered weighted non-oscillatory WENO reconstruction in which the choice of ideal weights has no influence on the properties of discretization: the ideal weights are symmetric and free from the regularity of the mesh and the scheme remains monotone even on a non-uniform grid.…”

Section: Introductionmentioning

confidence: 99%

Central WENO scheme for the integral form of contravariant shallow‐water equations

Gallerano

Cannata

2010

Numerical Methods in Fluids

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A new Central Weighted Essentially Non-Oscillatory scheme for the solution of the shallow-water equations expressed in contravariant formulation is presented. One of the most efficient methodologies belonging to Central WENO family involves: reconstructions of cell-averaged values of flow variables, reconstruction of point-values of flow variables, advancing from time level t(n) to time level t(n+1) of the cell-averaged values. The extension of the above-mentioned methodology into the contravariant environment implies that the contravariant shallow-water equations must be expressed in an integral form. An element of novelty presented in this paper regards the definition of a formal integral expression of the shallow-water equations in a contravariant formulation, in which the Christoffel symbols are avoided. The WENO reconstructions are performed by a two-dimensional interpolating procedure taking into account the curved coordinate lines. The proposed scheme ensures the satisfaction of the exact C-property. Several two-dimensional test cases are used to verify the good resolution for smooth and discontinuous solutions. Copyright (C) 2010 John Wiley & Sons, Ltd

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A central WENO scheme for solving hyperbolic conservation laws on non-uniform meshes

Cited by 108 publications

References 21 publications

Characteristic-based finite volume scheme for 1D Euler equations

Characteristic-based finite volume scheme for 1D Euler equations

Novel Slope Source Term Treatment for Preservation of Quiescent Steady States in Shallow Water Flows

Central WENO scheme for the integral form of contravariant shallow‐water equations

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