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

Lu, Changna; Qiu, Jianxian; Wang, Ruyun

doi:10.4208/jcm.1001-m3122

Cited by 9 publications

(5 citation statements)

References 26 publications

(42 reference statements)

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“…Bermudez and Vazquez [3] first introduced a concept of the "exact C-property". Since then, a number of well-balanced numerical methods have been developed for the SWEs, e.g., finite volume methods [1,3,22,44], finite difference/volume WENO methods [24,[34][35][36], and discontinuous Galerkin (DG) methods [9,10,12,13,23,33,[35][36][37][38].…”

Section: B(x Y)mentioning

confidence: 99%

A Well-Balanced Positivity-Preserving Quasi-Lagrange Moving Mesh DG Method for the Shallow Water Equations

Zhang¹,

Huang²,

Qiu³

2022

CICP

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A high-order, well-balanced, positivity-preserving quasi-Lagrange moving mesh DG method is presented for the shallow water equations with non-flat bottom topography. The well-balance property is crucial to the ability of a scheme to simulate perturbation waves over the lake-at-rest steady state such as waves on a lake or tsunami waves in the deep ocean. The method combines a quasi-Lagrange moving mesh DG method, a hydrostatic reconstruction technique, and a change of unknown variables. The strategies in the use of slope limiting, positivity-preservation limiting, and change of variables to ensure the well-balance and positivity-preserving properties are discussed. Compared to rezoning-type methods, the current method treats mesh movement continuously in time and has the advantages that it does not need to interpolate flow variables from the old mesh to the new one and places no constraint for the choice of a update scheme for the bottom topography on the new mesh. A selection of one-and two-dimensional examples are presented to demonstrate the wellbalance property, positivity preservation, and high-order accuracy of the method and its ability to adapt the mesh according to features in the flow and bottom topography.

show abstract

Section: B(x Y)mentioning

confidence: 99%

A Well-Balanced Positivity-Preserving Quasi-Lagrange Moving Mesh DG Method for the Shallow Water Equations

Zhang¹,

Huang²,

Qiu³

2022

CICP

View full text Add to dashboard Cite

show abstract

“…Bermudez and Vazquez [3] first introduced a concept of the "exact C-property". Since then, a number of well-balanced numerical methods have been developed for the SWEs, e.g., finite volume methods [1,3,18,38], finite difference/volume WENO methods [20,28,29,30], and discontinuous Galerkin (DG) methods [9,10,19,27,29,30,31,32]. DG methods have the advantages of highorder accuracy, high parallel efficiency, and flexibility for hp-adaptivity and arbitrary geometry and meshes.…”

Section: B(x Y)mentioning

confidence: 99%

A well-balanced positivity-preserving quasi-Lagrange moving mesh DG method for the shallow water equations

Zhang,

Huang,

Qiu

2020

Preprint

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A high-order, well-balanced, positivity-preserving quasi-Lagrange moving mesh DG method is presented for the shallow water equations with non-flat bottom topography. The well-balance property is crucial to the ability of a scheme to simulate perturbation waves over the lake-at-rest steady state such as waves on a lake or tsunami waves in the deep ocean. The method combines a quasi-Lagrange moving mesh DG method, a hydrostatic reconstruction technique, and a change of unknown variables. The strategies in the use of slope limiting, positivity-preservation limiting, and change of variables to ensure the well-balance and positivity-preserving properties are discussed. Compared to rezoning-type methods, the current method treats mesh movement continuously in time and has the advantages that it does not need to interpolate flow variables from the old mesh to the new one and places no constraint for the choice of an update scheme for the bottom topography on the new mesh. A selection of one-and two-dimensional examples are presented to demonstrate the well-balance property, positivity preservation, and high-order accuracy of the method and its ability to adapt the mesh according to features in the flow and bottom topography.

show abstract

“…Thus, in this paper, we mainly discuss finite volume WENO scheme in space as it is more flexible than finite difference scheme. We follow the same ideas of the previous papers [46,47] about finite volume WENO schemes.…”

Section: Scope and Contribution Of This Studymentioning

confidence: 99%

The Finite Volume WENO with Lax–Wendroff Scheme for Nonlinear System of Euler Equations

Dong

Yang

2018

Mathematics

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We develop a Lax–Wendroff scheme on time discretization procedure for finite volume weighted essentially non-oscillatory schemes, which is used to simulate hyperbolic conservation law. We put more focus on the implementation of one-dimensional and two-dimensional nonlinear systems of Euler functions. The scheme can keep avoiding the local characteristic decompositions for higher derivative terms in Taylor expansion, even omit partly procedure of the nonlinear weights. Extensive simulations are performed, which show that the fifth order finite volume WENO (Weighted Essentially Non-oscillatory) schemes based on Lax–Wendroff-type time discretization provide a higher accuracy order, non-oscillatory properties and more cost efficiency than WENO scheme based on Runge–Kutta time discretization for certain problems. Those conclusions almost agree with that of finite difference WENO schemes based on Lax–Wendroff time discretization for Euler system, while finite volume scheme has more flexible mesh structure, especially for unstructured meshes.

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

Cited by 9 publications

References 26 publications

A Well-Balanced Positivity-Preserving Quasi-Lagrange Moving Mesh DG Method for the Shallow Water Equations

A Well-Balanced Positivity-Preserving Quasi-Lagrange Moving Mesh DG Method for the Shallow Water Equations

A well-balanced positivity-preserving quasi-Lagrange moving mesh DG method for the shallow water equations

The Finite Volume WENO with Lax–Wendroff Scheme for Nonlinear System of Euler Equations

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