Positivity-preserving high order well-balanced discontinuous Galerkin methods for the shallow water equations

Advances in Water Resources ◽

10.1016/j.advwatres.2010.08.005 ◽

2010 ◽

Vol 33 (12) ◽

pp. 1476-1493 ◽

Author(s):

Yulong Xing ◽

Xiangxiong Zhang ◽

Chi-Wang Shu

Keyword(s):

Shallow Water ◽

Discontinuous Galerkin ◽

Shallow Water Equations ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Positivity Preserving

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Positivity-Preserving Well-Balanced Arbitrary Lagrangian–Eulerian Discontinuous Galerkin Methods for the Shallow Water Equations

Journal of Scientific Computing ◽

10.1007/s10915-021-01578-w ◽

2021 ◽

Vol 88 (3) ◽

Author(s):

Weijie Zhang ◽

Yinhua Xia ◽

Yan Xu

Keyword(s):

Shallow Water ◽

Discontinuous Galerkin ◽

Shallow Water Equations ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Arbitrary Lagrangian Eulerian ◽

Positivity Preserving

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Positivity-Preserving Well-Balanced Discontinuous Galerkin Methods for the Shallow Water Equations on Unstructured Triangular Meshes

Journal of Scientific Computing ◽

10.1007/s10915-013-9695-y ◽

2013 ◽

Vol 57 (1) ◽

pp. 19-41 ◽

Author(s):

Yulong Xing ◽

Xiangxiong Zhang

Keyword(s):

Shallow Water ◽

Discontinuous Galerkin ◽

Shallow Water Equations ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Triangular Meshes ◽

Positivity Preserving

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Nodal High-Order Discontinuous Galerkin Methods for the Spherical Shallow Water Equations

Journal of Computational Physics ◽

10.1006/jcph.2002.7139 ◽

2002 ◽

Vol 181 (2) ◽

pp. 499-525 ◽

Author(s):

F.X. Giraldo ◽

J.S. Hesthaven ◽

T. Warburton

Keyword(s):

Shallow Water ◽

Discontinuous Galerkin ◽

Shallow Water Equations ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods

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High order well-balanced discontinuous Galerkin methods based on hydrostatic reconstruction for shallow water equations

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2017.10.027 ◽

2018 ◽

Vol 340 ◽

pp. 546-560 ◽

Author(s):

Gang Li ◽

Lina Song ◽

Jinmei Gao

Keyword(s):

Shallow Water ◽

Discontinuous Galerkin ◽

Shallow Water Equations ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods

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Nodal High-Order Discontinuous Galerkin Methods for the Spherical Shallow Water Equations

10.21236/ada633613 ◽

2002 ◽

Author(s):

F. X. Giraldo ◽

J. S. Hesthaven ◽

T. Warburton

Keyword(s):

Shallow Water ◽

Discontinuous Galerkin ◽

Shallow Water Equations ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods

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High order sign-preserving and well-balanced exponential Runge-Kutta discontinuous Galerkin methods for the shallow water equations with friction

Journal of Computational Physics ◽

10.1016/j.jcp.2021.110543 ◽

2021 ◽

pp. 110543

Author(s):

Ruize Yang ◽

Yang Yang ◽

Yulong Xing

Keyword(s):

Shallow Water ◽

Discontinuous Galerkin ◽

Shallow Water Equations ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

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High-order entropy stable discontinuous Galerkin methods for the shallow water equations: Curved triangular meshes and GPU acceleration

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2020.11.006 ◽

2021 ◽

Vol 82 ◽

pp. 179-199

Author(s):

Xinhui Wu ◽

Ethan J. Kubatko ◽

Jesse Chan

Keyword(s):

Shallow Water ◽

Discontinuous Galerkin ◽

Shallow Water Equations ◽

Discontinuous Galerkin Methods ◽

Gpu Acceleration ◽

Galerkin Methods ◽

Triangular Meshes ◽

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High-order discontinuous element-based schemes for the inviscid shallow water equations: Spectral multidomain penalty and discontinuous Galerkin methods

Applied Mathematics and Computation ◽

10.1016/j.amc.2011.10.046 ◽

2012 ◽

Vol 218 (9) ◽

pp. 4825-4848 ◽

Author(s):

J.A. Escobar-Vargas ◽

P.J. Diamessis ◽

F.X. Giraldo

Keyword(s):

Shallow Water ◽

Discontinuous Galerkin ◽

Shallow Water Equations ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods

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A Comparison of the Explicit and Implicit Hybridizable Discontinuous Galerkin Methods for Nonlinear Shallow Water Equations

Journal of Scientific Computing ◽

10.1007/s10915-019-01007-z ◽

2019 ◽

Vol 80 (3) ◽

pp. 1936-1956 ◽

Author(s):

Ali Samii ◽

Kazbek Kazhyken ◽

Craig Michoski ◽

Clint Dawson

Keyword(s):

Shallow Water ◽

Discontinuous Galerkin ◽

Shallow Water Equations ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Hybridizable Discontinuous Galerkin ◽

Nonlinear Shallow Water Equations ◽

Hybridizable Discontinuous Galerkin Methods

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Exactly well-balanced discontinuous Galerkin methods for the shallow water equations with moving water equilibrium

Journal of Computational Physics ◽

10.1016/j.jcp.2013.10.010 ◽

2014 ◽

Vol 257 ◽

pp. 536-553 ◽

Author(s):

Yulong Xing

Keyword(s):

Shallow Water ◽

Discontinuous Galerkin ◽

Shallow Water Equations ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Water Equilibrium

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