A Comparative Study between Finite Difference Method and Finite Volume Method for Shallow Water-Dam Break Flow Problem

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M. M. Rahaman
M. M. Rahaman
1 Jahangirnagar University

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A Comparative Study between Finite Difference Method and Finite Volume Method for Shallow Water-Dam Break Flow Problem Banner
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In this paper we perform numerical simulation of shallow water equations for dam break flow problem. Finite difference method and finite volume method are applied for the numerical solution of the shallow water equations. We estimate water height and water velocity for the test case of shallow waterdam break flow problem at different height ratio. The comparisons between the finite difference method and finite volume method for 1-D dam break problem have been shown. The agreement of numerical solution with analytic solution by finite volume method is better than finite difference method. We compare the computational efficiency for both schemes in subcritical flow.

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References

  1. V Bellos,V Hrissanthou (2011). Numerical simulation of Dam break flood wave.
  2. Fayssal Benkhaldoun,Mohammed Seaïd (2010). A simple finite volume method for the shallow water equations.
  3. J Stoker (1986). Water Waves.
  4. M Rahaman,L Andallah,M Alam (2017). Numerical solution of advection diffusion reaction equation coupled with shallow water equations.
  5. Jafar Baghari,K Samir,Das (2013). Modeling of shallow water equations by using implicit high order compact scheme with application to dam break problem.
  6. K Samir,Jafar Das,Baghari (2015). Modeling of shallow water equations by using compact Mac-Cormack type schemes with application to dam break problem.
  7. Md,Saiduzzaman,Kumar Sobuj,Ray (2013). Comparison of numerical schemes for shallow water equation.
  8. M Ahmed,M Mamat,W Wan Nik,A Kartono (2013). Numerical method for dam break problem by using Godunov approach.
  9. Randall Leveque (1992). Numerical methods for conservation laws.
  10. Pilar García-Navarro,Pilar Brufau One Dimensional Dam Break Flow Modeling.

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

M. M. Rahaman. 2019. \u201cA Comparative Study between Finite Difference Method and Finite Volume Method for Shallow Water-Dam Break Flow Problem\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 19 (GJSFR Volume 19 Issue F3): .

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Issue Cover
GJSFR Volume 19 Issue F3
Pg. 67- 74
Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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GJSFR-F Classification: MSC 2010: 65L12
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v1.2

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August 19, 2019

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English

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In this paper we perform numerical simulation of shallow water equations for dam break flow problem. Finite difference method and finite volume method are applied for the numerical solution of the shallow water equations. We estimate water height and water velocity for the test case of shallow waterdam break flow problem at different height ratio. The comparisons between the finite difference method and finite volume method for 1-D dam break problem have been shown. The agreement of numerical solution with analytic solution by finite volume method is better than finite difference method. We compare the computational efficiency for both schemes in subcritical flow.

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A Comparative Study between Finite Difference Method and Finite Volume Method for Shallow Water-Dam Break Flow Problem

M. M. Rahaman
M. M. Rahaman Jahangirnagar University

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