SEMI-IMPLICIT NUMERICAL SCHEMA IN SHALLOW WATER EQUATION

Abstract. A two-dimensional shallow water equation integrated on depth water based on finite differential methods. Numerical solutions with different methods consist of explicit, implicit and semi-implicit schemes. Different methods of shallow water equations expressed in numerical schemes. For bottom-friction is described in semi-implicitly. This scheme will be more flexible for initial values and boundary conditions when compared to the explicit schemes. Keywords: 2D numerical models, shallow water equations, explicit and semi-implicit schema.Reference Hassan, H. S., Ramadan, K. T., Hanna, S. N. 2010. Numerical Solution of the Rotating Shallow Water Flows with Topography Using the Fractional Steps Method, Scie.Res,App.Math. (1):104-117. Omer, S, Kursat, K. 2011. High-Order Accurate Spectral Difference Method For Shallow Water Equations. IJRRAS6. Vol. 6. No. 1. Kampf, J. 2009. Ocean Modelling for Beginners. Springer Heidelberg Dordrecht. London, New York. Wang, Z. L., Geng, Y. F. 2013. Two-Dimensional Shallow Water Equations with Porosity and Their Numerical scheme on Unstructured Grids. J. Water Science and Engineering. Vol. 6, No. 1, 91-105. Saiduzzaman, Sobuj. 2013. Comparison of Numerical Schemes for Shallow Water Equation. Global J. of Sci. Fron. Res. Math. and Dec. Sci. Vol. 13 (4). Sari, C. I., Surbakti, H., Fauziyah., Pola Sebaran Salinatas dengan Model Numerik Dua Dimensi di Muara Sungai Musi. Maspari J. Vol. 5 (2): 104-110. Bunya, B., Westerink, J. J. dan Shinobu, Y. 2004. Discontinuous Boundary Implementation for the Shallow Water Equations. Int. J. Numer. Meth. Fluids 2005 (47): 1451–1468.

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Weak Local Residuals as Smoothness Indicators in Adaptive Mesh Methods for Shallow Water Flows

Symmetry ◽

10.3390/sym12030345 ◽

2020 ◽

Vol 12 (3) ◽

pp. 345

Author(s):

Sudi Mungkasi ◽

Stephen Gwyn Roberts

Keyword(s):

Shallow Water ◽

Shallow Water Equations ◽

Numerical Solutions ◽

Adaptive Mesh ◽

Finite Volume Methods ◽

Water Type ◽

Two Dimensional ◽

Water Flows ◽

Shallow Water Flows ◽

Smoothness Indicators

This paper proposes some formulations of weak local residuals of shallow-water-type equations, namely, one-, one-and-a-half-, and two-dimensional shallow water equations. Smooth parts of numerical solutions have small absolute values of weak local residuals. Rougher parts of numerical solutions have larger absolute values of weak local residuals. This behaviour enables the weak local residuals to detect parts of numerical solutions which are smooth and rough (non-smooth). Weak local residuals that we formulate are implemented successfully as refinement or coarsening indicators for adaptive mesh finite volume methods used to solve shallow water equations.

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High Order Two Dimensional Numerical Schemes for the Coupling of Transport Equations and Shallow Water Equations

Numerical Mathematics and Advanced Applications ◽

10.1007/978-3-540-69777-0_28 ◽

2008 ◽

pp. 241-248

Author(s):

M. J. Castro ◽

E. D. Fernández Nieto ◽

A. M. Ferreiro Ferreiro ◽

J. A. García Rodríguez ◽

C. Parés

Keyword(s):

Shallow Water ◽

Shallow Water Equations ◽

Transport Equations ◽

High Order ◽

Two Dimensional ◽

Numerical Schemes

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Maximum power from a turbine farm in shallow water

Journal of Fluid Mechanics ◽

10.1017/jfm.2012.515 ◽

2013 ◽

Vol 714 ◽

pp. 634-643 ◽

Cited By ~ 20

Author(s):

Chris Garrett ◽

Patrick Cummins

Keyword(s):

Shallow Water ◽

Shallow Water Equations ◽

Numerical Solutions ◽

Momentum Equation ◽

Basic Flow ◽

Maximum Power ◽

Two Dimensional ◽

Dominant Term ◽

Tidal Flows ◽

Linear Friction

AbstractThe maximum power that can be obtained from a confined array of turbines in steady or tidal flows is considered using the two-dimensional shallow-water equations and representing the turbine farm by a uniform local increase in friction within a circle. Analytical results supported by dimensional reasoning and numerical solutions show that the maximum power depends on the dominant term in the momentum equation for flows perturbed on the scale of the farm. If friction dominates in the basic flow, the maximum power is a fraction (half for linear friction and 0.75 for quadratic friction) of the dissipation within the circle in the undisturbed state; if the advective terms dominate, the maximum power is a fraction of the undisturbed kinetic energy flux into the front of the turbine farm; if the acceleration dominates, the maximum power is similar to that for the linear frictional case, but with the friction coefficient replaced by twice the tidal frequency.

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SHALLOW WATER EQUATION SOLUTION IN 2D USING FINITE DIFFERENCE METHOD WITH EXPLICIT SCHEME

Jurnal Natural ◽

10.24815/jn.v17i2.7997 ◽

2017 ◽

Vol 17 (2) ◽

pp. 105

Author(s):

Nuraini Nuraini ◽

Syamsul Rizal ◽

Marwan Marwan

Keyword(s):

Finite Difference ◽

Shallow Water ◽

Shallow Water Equations ◽

Shallow Water Equation ◽

Mass Conservation ◽

Conservation Equation ◽

Water Model ◽

Two Dimensional ◽

Shallow Water Model ◽

Three Dimensional Model

Abstract. Modeling the dynamics of seawater typically uses a shallow water model. The shallow water model is derived from the mass conservation equation and the momentum set into shallow water equations. A two-dimensional shallow water equation alongside the model that is integrated with depth is described in numerical form. This equation can be solved by finite different methods either explicitly or implicitly. In this modeling, the two dimensional shallow water equations are described in discrete form using explicit schemes.Keyword: shallow water equation, finite difference and schema explisit.REFERENSI 1. Bunya, S., Westerink, J. J. dan Yoshimura. 2005. Discontinuous Boundary Implementation for the Shallow Water Equations. Int. J. Numer. Meth. Fluids. 47: 1451-1468.2. Kampf Jochen. 2009. Ocean Modelling For Beginners. Springer Heidelberg Dordrecht. London New York.3. Rezolla, L 2011. Numerical Methods for the Solution of Partial Diferential Equations. Trieste. International Schoolfor Advanced Studies.4. Natakussumah, K. D., Kusuma, S. B. M., Darmawan, H., Adityawan, B. M. Dan Farid, M. 2007. Pemodelan Hubungan Hujan dan Aliran Permukaan pada Suatu DAS dengan Metode Beda Hingga. ITB Sain dan Tek. 39: 97-123.5. Casulli, V. dan Walters, A. R. 2000. An unstructured grid, three-dimensional model based on the shallow water equations. Int. J. Numer. Meth. Fluids. 32: 331-348.6. Triatmodjo, B. 2002. Metode Numerik Beta Offset. Yogyakarta.

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Modelling Weirs in Two-Dimensional Shallow Water Models

Water ◽

10.3390/w13162152 ◽

2021 ◽

Vol 13 (16) ◽

pp. 2152

Author(s):

Gonzalo García-Alén ◽

Olalla García-Fonte ◽

Luis Cea ◽

Luís Pena ◽

Jerónimo Puertas

Keyword(s):

Experimental Data ◽

Shallow Water ◽

Shallow Water Equations ◽

Water Model ◽

Two Dimensional ◽

Shallow Water Model ◽

Experimental Dataset ◽

River Hydraulics ◽

Shallow Water Models ◽

Water Models

2D models based on the shallow water equations are widely used in river hydraulics. However, these models can present deficiencies in those cases in which their intrinsic hypotheses are not fulfilled. One of these cases is in the presence of weirs. In this work we present an experimental dataset including 194 experiments in nine different weirs. The experimental data are compared to the numerical results obtained with a 2D shallow water model in order to quantify the discrepancies that exist due to the non-fulfillment of the hydrostatic pressure hypotheses. The experimental dataset presented can be used for the validation of other modelling approaches.

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