Implementasi Skema Collocated Semi-implicit untuk SWE-Exner menggunakan Fluks HLLE

  • Ardhito Utomo Telkom University
  • Putu Harry Gunawan Telkom University
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Pada naskah ini simulasi persamaan Shallow Water - Exner dilakukan. Naskah ini menjabarkan bahwa penggabungan persaamaan antara Shallow Water dan Exner dapat dilakukan menggunakan teknik splitting, yaitu setelah ditemukannya nilai dari SWE menggunakan fluks numerik, persamaan Exner dicari secara semi-implicit. Fluks numerik Harten-Lax-van Leer and Einfeld digunakan. Naskah ini menjelaskan langkah-langkah dalam pembentukkan simulasi Shallow Water Equation - Exner: pencarian SWE, Exner, nilai fluks, dan juga penggunaan friksi pada simulasi. Setelah itu, diselesaikan beberapa kasus untuk membuktikan hasil simulasi. Dari hasil simulasi dapat dilihat bahwa simulasi menghasilkan bentuk yang sesuai dengan naskah yang dibandingkan.


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Christophe Ancey. Stochastic modeling in sediment dynamics: Exner equation for planar bed incipient bed load transportconditions.Journal of Geophysical Research: Earth Surface, 115(F2), 2010.

Emmanuel Audusse, Christophe Berthon, Christophe Chalons, Olivier Delestre, Nicole Goutal, Magali Jodeau, Jacques Sainte-Marie, Jan Giesselmann, and Georges Sadaka. Sediment transport modelling: Relaxation schemes for saint-venant–exner andthree layer models. InESAIM: proceedings, volume 38, pages 78–98. EDP Sciences, 2012.

Emmanuel Audusse and Marie-Odile Bristeau. Finite-volume solvers for a multilayer saint-venant system.InternationalJournal of Applied Mathematics and Computer Science, 17(3):311–320, 2007.

Christophe Berthon, Stéphane Cordier, Olivier Delestre, and Minh Hoang Le. An analytical solution of the shallow watersystem coupled to the exner equation.Comptes Rendus Mathematique, 350(3):183–186, 2012.

Christophe Berthon and Fabien Marche. A positive preserving high order vfroe scheme for shallow water equations: a classof relaxation schemes.SIAM Journal on Scientific Computing, 30(5):2587–2612, 2008

Francois Bouchut.Nonliniear Stability of Finite Volume Methods for Hyperbolic Conservation Laws and Well-BalancedSchemes for Sources. Birkhauser, 2000.

François Bouchut, Julien Le Sommer, and Vladimir Zeitlin. Frontal geostrophic adjustment and nonlinear wave phenomena inone-dimensional rotating shallow water. part 2. high-resolution numerical simulations.Journal of Fluid Mechanics, 514:35–63,2004.

Zhixian Cao, Gareth Pender, and Jian Meng. Explicit formulation of the shields diagram for incipient motion of sediment.Journal of Hydraulic Engineering, 132(10):1097–1099, 2006.

SE Coleman and VI Nikora. Exner equation: A continuum approximation of a discrete granular system.Water ResourcesResearch, 45(9), 2009.

Stéphane Cordier, Minh H Le, and T Morales De Luna. Bedload transport in shallow water models: Why splitting (may)fail, how hyperbolicity (can) help.Advances in Water Resources, 34(8):980–989, 2011.

Olivier Delestre, Stéphane Cordier, Frédéric Darboux, and Francois James. A limitation of the hydrostatic reconstructiontechnique for shallow water equations.Comptes Rendus Mathematique, 350(13-14):677–681, 2012.

MJ Castro Díaz, Enrique D Fernández-Nieto, and AM Ferreiro. Sediment transport models in shallow water equations andnumerical approach by high order finite volume methods.Computers & Fluids, 37(3):299–316, 2008.

Putu Harry Gunawan. Numerical simulation of tsunami hazard mitigation by mangrove forest in north coast bali, indonesia.Jurnal Matematika, 5(1):1–13, 2015.

Putu Harry Gunawan, R Eymard, and SR Pudjaprasetya.Staggered scheme for the exner–shallow water equations.Computational Geosciences, 19(6):1197–1206, 2015.

Putu Harry Gunawan and Xavier Lhébrard. Hydrostatic relaxation scheme for the 1d shallow water-exner equations in bedloadtransport.Computers & Fluids, 121:44–50, 2015.

Robert H Kadlec. Overland flow in wetlands: vegetation resistance.Journal of Hydraulic Engineering, 116(5):691–706, 1990.

John Nicholas Newman and John Grue.Marine hydrodynamics. MIT press, 2018.

Guy Simpson and Sébastien Castelltort. Coupled model of surface water flow, sediment transport and morphological evolution.Computers & Geosciences, 32(10):1600–1614, 2006

How to Cite
Utomo, A., & Gunawan, P. H. (2018). Implementasi Skema Collocated Semi-implicit untuk SWE-Exner menggunakan Fluks HLLE. Indonesian Journal on Computing (Indo-JC), 3(1), 85-96.
Computer Science