Proceedings of the 7th Mathematics, Science, and Computer Science Education International Seminar, MSCEIS 2019, 12 October 2019, Bandung, West Java, Indonesia

Research Article

A Modified Lax-Friedrichs Method for the Shallow Water Equations

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  • @INPROCEEDINGS{10.4108/eai.12-10-2019.2296327,
        author={Kartika  Yulianti and Rini  Marwati and Suci  Permatahati},
        title={A Modified Lax-Friedrichs Method for the Shallow Water Equations},
        proceedings={Proceedings of the 7th Mathematics, Science, and Computer Science Education International Seminar, MSCEIS 2019, 12 October 2019, Bandung, West Java, Indonesia},
        publisher={EAI},
        proceedings_a={MSCEIS},
        year={2020},
        month={7},
        keywords={shallow water equations lax-friedrichs method modification},
        doi={10.4108/eai.12-10-2019.2296327}
    }
    
  • Kartika Yulianti
    Rini Marwati
    Suci Permatahati
    Year: 2020
    A Modified Lax-Friedrichs Method for the Shallow Water Equations
    MSCEIS
    EAI
    DOI: 10.4108/eai.12-10-2019.2296327
Kartika Yulianti1,*, Rini Marwati1, Suci Permatahati1
  • 1: Department of Mathematics Education, Universitas Pendidikan Indonesia (UPI), Jl. Dr. Setiabudi no 229 Bandung 40154, Indonesia
*Contact email: kartika.yulianti@upi.edu

Abstract

In this paper, we present a simple modified Lax-Friedrichs method for the numerical solution of shallow water equations. In the proposed method, we approximate the next-step value by applying the Lax–Friedrichs method at the half grid of space. The method was applied to simulate the wave propagation at a resting pool for non-flat topography. Based on the simulation, the proposed method is more accurate in terms of fulfilling the conservation law than the Lax-Friedrichs method and it shows good agreement with the steady analytical solution