Numerical Simulation of the Ripa Model using the Upwind CE/SE Scheme

Authors

  • Saqib Zia Department of Mathematics, COMSATS University Islamabad, Park Road, Chak Shahzad Islamabad, Pakistan
  • Asad Rehman Department of Computer Science, Air University, Kharian Campus Pakistan
  • Samina Majeed Department of Mathematics, COMSATS University Islamabad, Park Road, Chak Shahzad Islamabad, Pakistan
  • Abuzar Ghaffari Department of Mathematics, COMSATS University Islamabad, Park Road, Chak Shahzad Islamabad, Pakistan
  • Shagufta Yasmeen Department of Mathematics, COMSATS University Islamabad, Park Road Chak Shehzad, 7 Islamabad, Pakistan
  • Wei Sin Koh International University, Persiaran Perdana BBN Putra Nilai, 71800 Nilai, Negeri Sembilan, Malaysia
  • Ilyas Khan Department of Mathematical Sciences, Saveetha School of Engineering, SIMATS, Chennai, Tamil Nadu, India; Hourani Center for Applied scientific Research, Al-Ahliyya Amman University, Amman, Jordan; Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i4.6230

Keywords:

Ripa model, Non-conservative systems, Horizontal temperature gradient, Bottom topography, Upwind CE/SE scheme \sep CE/SE scheme \sep Smart grid

Abstract

This paper focuses on the numerical investigation of the shallow water equations (SWEs) with temperature gradients, commonly referred to as the Ripa system, using the finite volume upwind Conservation Element Solution Element (CE/SE) scheme. The inclusion of source-term on the right-hand side of the model introduces additional complexity, making the equations non-conservative and challenging to solve numerically. The primary objective is to develop a numerical scheme that effective ly handles non-conservative differential terms with accuracy and efficiency. To address these challenges, a finite volume upwind CE/SE technique is proposed. The method is tested on several numerical problems to evaluate its effectiveness, robustness, and stability, particularly in resolving discontinuities and shocks. The results of the proposed scheme are compared with those obtained using the standard CE/SE scheme.  

Author Biography

  • Ilyas Khan, Department of Mathematical Sciences, Saveetha School of Engineering, SIMATS, Chennai, Tamil Nadu, India; Hourani Center for Applied scientific Research, Al-Ahliyya Amman University, Amman, Jordan; Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia
    Department of Mathematical Sciences, Saveetha School of Engineering, SIMATS, Chennai, Tamil Nadu, India; Hourani Center for Applied scientific Research, Al-Ahliyya Amman University, Amman, Jordan; Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia

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Published

2025-11-05

Issue

Vol. 18 No. 4: (October 2025)

Section

Partial Differential Equations and Dynamical Systems

License

Copyright (c) 2025 Saqib Zia, Asad Rehman, Samina Majeed, Abuzar Ghaffari, Shagufta Yasmeen, Wei Sin Koh, Ilyas Khan

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How to Cite

Numerical Simulation of the Ripa Model using the Upwind CE/SE Scheme. (2025). European Journal of Pure and Applied Mathematics, 18(4), 6230. https://doi.org/10.29020/nybg.ejpam.v18i4.6230