A Positivity-Preserving Well-Balanced Central Discontinuous Galerkin Method for the Nonlinear Shallow Water Equations

被引：36

作者：

Li, Maojun ^{[1
,2
]}

Guyenne, Philippe ^{[3
]}

Li, Fengyan ^{[4
]}

Xu, Liwei ^{[1
,2
,5
]}

机构：

[1] Chongqing Univ, Coll Math & Stat, Chongqing 401331, Peoples R China

[2] Chongqing Univ, Inst Comp & Data Sci, Chongqing 400044, Peoples R China

[3] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

[4] Rensselaer Polytech Inst, Dept Math Sci, Troy, NY 12180 USA

[5] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 611731, Sichuan, Peoples R China

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2017年 / 71卷 / 03期

基金：

美国国家科学基金会;

关键词：

Central discontinuous Galerkin methods; High-order accuracy; Nonlinear shallow water equations; Positivity-preserving property; Well-balanced schemes; DIFFERENCE WENO SCHEMES; CENTRAL-UPWIND SCHEME; HYPERBOLIC SYSTEMS; CONSERVATION-LAWS; SOURCE TERMS; SOLVERS; WAVES;

D O I：

10.1007/s10915-016-0329-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the development of central discontinuous Galerkin methods for solving the nonlinear shallow water equations over variable bottom topography in one and two dimensions. A reliable numerical scheme for these equations should preserve still-water stationary solutions and maintain the non-negativity of the water depth. We propose a high-order technique which exactly balances the flux gradients and source terms in the still-water stationary case by adding correction terms to the base scheme, meanwhile ensures the non-negativity of the water depth by using special approximations to the bottom together with a positivity-preserving limiter. Numerical tests are presented to illustrate the accuracy and validity of the proposed schemes.

引用

页码：994 / 1034

页数：41

共 50 条

[1] A Positivity-Preserving Well-Balanced Central Discontinuous Galerkin Method for the Nonlinear Shallow Water Equations
Maojun Li
Philippe Guyenne
Fengyan Li
Liwei Xu
[J]. Journal of Scientific Computing, 2017, 71 : 994 - 1034
[2] A modified central discontinuous Galerkin method with positivity-preserving and well-balanced properties for the one-dimensional nonlinear shallow water equations
Chen, Aimin
Li, Maojun
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2019, 345 : 374 - 387
[3] Positivity-preserving high order well-balanced discontinuous Galerkin methods for the shallow water equations
Xing, Yulong
Zhang, Xiangxiong
Shu, Chi-Wang
[J]. ADVANCES IN WATER RESOURCES, 2010, 33 (12) : 1476 - 1493
[4] Positivity-Preserving Well-Balanced Discontinuous Galerkin Methods for the Shallow Water Equations on Unstructured Triangular Meshes
Yulong Xing
Xiangxiong Zhang
[J]. Journal of Scientific Computing, 2013, 57 : 19 - 41
[5] Positivity-Preserving Well-Balanced Arbitrary Lagrangian–Eulerian Discontinuous Galerkin Methods for the Shallow Water Equations
Weijie Zhang
Yinhua Xia
Yan Xu
[J]. Journal of Scientific Computing, 2021, 88
[6] Positivity-Preserving Well-Balanced Discontinuous Galerkin Methods for the Shallow Water Equations on Unstructured Triangular Meshes
Xing, Yulong
Zhang, Xiangxiong
[J]. JOURNAL OF SCIENTIFIC COMPUTING, 2013, 57 (01) : 19 - 41
[7] A well-balanced positivity-preserving multidimensional central scheme for shallow water equations
Yan, Ruifang
Tong, Wei
Chen, Guoxian
[J]. APPLIED NUMERICAL MATHEMATICS, 2024, 197 : 97 - 118
[8] Positivity-Preserving Well-Balanced Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Methods for the Shallow Water Equations
Zhang, Weijie
Xia, Yinhua
Xu, Yan
[J]. JOURNAL OF SCIENTIFIC COMPUTING, 2021, 88 (03)
[9] Positivity-preserving well-balanced discontinuous Galerkin methods for the shallow water flows in open channels
Qian, Shouguo
Li, Gang
Shao, Fengjing
Xing, Yulong
[J]. ADVANCES IN WATER RESOURCES, 2018, 115 : 172 - 184
[10] Application of positivity-preserving well-balanced discontinuous Galerkin method in computational hydrology
Wen, Xiao
Gao, Zhen
Don, Wai Sun
Xing, Yulong
Li, Peng
[J]. COMPUTERS & FLUIDS, 2016, 139 : 112 - 119

← 1 2 3 4 5 →