Article: Numerical modelling of wave propagation in shallow water Journal: International Journal of Mathematical Modelling and Numerical Optimisation (IJMMNO) 2025 Vol.15 No.5 pp.1 - 15 Abstract: Coastal communities worldwide face significantly higher risks than their inland counterparts, primarily due to threats like tsunamis, dam failures, and storm surges. Identifying and addressing these hazards before they result in loss of life is paramount. This paper presents a numerical scheme developed in MATLAB to solve shallow water equations, offering a valuable tool for mitigating these critical threats. Traditionally, computational limitations in memory and speed have required the division of complex simulations into smaller, more manageable sections in computational fluid dynamics. While advancements in computational power have grown exponentially, so too has the complexity of the problems being addressed. The model employs finite difference methods to solve the shallow water equations, utilising user-defined parameters such as domain size, shape, grid resolution, and boundary conditions. It generates customised data and presents results through animated visualisations. The results from this model have shown promising potential, highlighting its ability to enhance understanding and mitigation strategies for coastal hazards significantly. Inderscience Publishers - linking academia, business and industry through research

Title: Numerical modelling of wave propagation in shallow water

Authors: Vetrichelvan Pugazendi; Efstratios L. Ntantis

Addresses: Cranfield University, College Rd., Wharley End, Bedford MK43 0AL, UK ' Amity University Dubai, International Academic City, Dubai 345019, UAE

Abstract: Coastal communities worldwide face significantly higher risks than their inland counterparts, primarily due to threats like tsunamis, dam failures, and storm surges. Identifying and addressing these hazards before they result in loss of life is paramount. This paper presents a numerical scheme developed in MATLAB to solve shallow water equations, offering a valuable tool for mitigating these critical threats. Traditionally, computational limitations in memory and speed have required the division of complex simulations into smaller, more manageable sections in computational fluid dynamics. While advancements in computational power have grown exponentially, so too has the complexity of the problems being addressed. The model employs finite difference methods to solve the shallow water equations, utilising user-defined parameters such as domain size, shape, grid resolution, and boundary conditions. It generates customised data and presents results through animated visualisations. The results from this model have shown promising potential, highlighting its ability to enhance understanding and mitigation strategies for coastal hazards significantly.

Keywords: coastal hazards; coastal fluid dynamics; mitigation strategies; shallow water equations; MATLAB simulation.

DOI: 10.1504/IJMMNO.2025.148206

International Journal of Mathematical Modelling and Numerical Optimisation, 2025 Vol.15 No.5, pp.1 - 15

Received: 01 Apr 2025
Accepted: 11 Jun 2025
Published online: 29 Aug 2025 *

Title: Numerical modelling of wave propagation in shallow water

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