A Staggered Method for Simulating Shallow Water Flows along Channels with Irregular Geometry and Friction
B. de Saint-Venant, “Théorie du Mouvement Non Permanent des Eaux, avec Application aux Crues des Rivières et à l’introduction des Marées dans leur Lit,” Comptes Rendus des Séances l’Académie des Sci., vol. 73, pp. 147–154, 237–240, 1871.
J. A. Cunge, F. M. Holly Jr, and A. Verwey, Practical Aspects of Computational River Hydraulics. Boston: Pitman Advanced Publishing Program, 1980.
K. Ostad-Ali-Askari, M. Shayannejad, S. Eslamian, and B. Navabpour, “Comparison of solutions of Saint-Venant equations by characteristics and finite difference methods for unsteady flow analysis in open channel,” Int. J. Hydrol. Sci. Technol., vol. 8, no. 3, pp. 229–243, 2018.
G. Natasha, Suharjito, and V. Noviantri, “Saint-Venant Model Analysis of Trapezoidal Open Channel Water Flow using Finite Difference Method,” Procedia Comput. Sci., vol. 157, pp. 6–15, 2019.
J. Balbás and S. Karni, “A Central Scheme for Shallow Water Flows along Channels with Irregular Geometry,” ESAIM Math. Model. Numer. Anal., vol. 38, pp. 821–852, 2004.
W. Lai and A. A. Khan, “Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method,” J. Hydrodyn., vol. 30, no. 2, pp. 189–202, 2018.
V. Michel-Dansac, C. Berthon, S. Clain, and F. Foucher, “A well-balanced scheme for the shallow-water equations with topography or Manning friction,” J. Comput. Phys., vol. 335, pp. 115–154, 2017.
S. Mungkasi, I. Magdalena, S. R. Pudjaprasetya, L. H. Wiryanto, and S. G. Roberts, “A staggered method for the shallow water equations involving varying channel width and topography,” Int. J. Multiscale Comput. Eng., vol. 16, no. 3, pp. 231–244, 2018.
X. Xia and Q. Liang, “A new efficient implicit scheme for discretising the stiff friction terms in the shallow water equations,” Adv. Water Resour., vol. 117, no. March, pp. 87–97, 2018.
G. S. Stelling and S. P. A. Duinmeijer, “A staggered conservative scheme for every Froude number in rapidly varied shallow water flows,” Int. J. Numer. Methods Fluids, vol. 43, no. 12, pp. 1329–1354, 2003.
R. J. LeVeque, Numerical Methods for Conservation Laws. Basel: Birkhäuser, 1992.
C. Lu, L. Xie, and H. Yang, “The Simple Finite Volume Lax-Wendroff Weighted Essentially Nonoscillatory Schemes for Shallow Water Equations with Bottom Topography,” Math. Probl. Eng., vol. 2018, 2018.
A. Kurganov, “Finite-volume schemes for shallow-water equations,” Acta Numer., vol. 27, pp. 289–351, 2018.
A. Kurganov, S. Noelle, and G. Petrova, “Semidiscrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton–Jacobi Equations,” SIAM J. Sci. Comput., vol. 23, no. 3, pp. 703–740, 2001.
S. Mungkasi, “A study of well-balanced finite volume methods and refinement indicators for the shallow water equations,” Bull. Aust. Math. Soc., vol. 88, no. 2, pp. 351–352, 2013.
S. Mungkasi, “Adaptive Finite Volume Method for the Shallow Water Equations on Triangular Grids,” Adv. Math. Phys., vol. 2016, no. October, 2016.
H. Ai, L. Yao, H. Zhao, and Y. Zhou, “Shallow-Water-Equation Model for Simulation of Earthquake-Induced Water Waves,” Math. Probl. Eng., vol. 2017, pp. 1–11, 2017.
B. A. Sulistyono and L. H. Wiryanto, “Investigation of flood routing by a dynamic wave model in trapezoidal channels Investigation of Flood Routing by a Dynamic Wave Model in Trapezoidal Channels,” in AIP Conference Proceedings, 2017, vol. 1867, no. August, pp. 0200201–8.
B. A. Sulistyono and L. H. Wiryanto, “An Analysis of the Influence of Variability Rainfall on Flow Rate Based on the Watershed Characteristics,” in IOP Conference Series: Earth and Environmental Science, 2018, vol. 124, no. 1, pp. 0–6.
J. Stoker, Water Waves: The Mathematical Theory with Applications. New York: Interscience Publishers, 1957.
N. Goutal and F. Maurel, “Proceedings of the 2nd Workshop on Dam-Break Wave Simulation,” in Technical Report HE-43/97/016/B, Electricité de France, Direction des études et recherches, Paris, 1997.
- There are currently no refbacks.
Published by INSIGHT - Indonesian Society for Knowledge and Human Development