1-D shallow water equation, with no viscosity and no rotation, for a topography represented by a quadratic function. (7th August 2020)

• Record Type: Journal Article
• Authors: Cortés-Vélez, Catalina; Martín-Atienza, Beatriz; Hernandez-Walls, Rafael
• Is Part Of: Journal of physics communications. Volume 4:Number 8(2020)
• Publication Date: 2020-08-07
• Subjects: partial derivative equations -- shallow water equations -- modeling bathymetry -- power series; Physics -- Periodicals; 530.05
• DOI: 10.1088/2399-6528/abaa8c
• Languages: English
• ISSNs: 2399-6528

Abstract

Abstract: Based on the linearized shallow water equations with no rotation and no viscosity, in a rectangular channel with topography, the analytical solution for elevation and velocity was obtained. The bathymetry of the rectangular channel is described by a quadratic function. The analytical solution was determined from generalized power series, resulting in numerically convergent power series. This methodology is a useful and easy tool, which can be used by teachers in the teaching of differential equations and modeling.