A Robust Well- Balanced Finite Volume Scheme for the One Dimensional Shallow Water

The aim of this study was building a finite volume approach for numerically solving one-dimensional shallow water equations, which applies to flat and non-flat terrain. The devised approach exhibits simplicity and accuracy throughout the time integration process. The proposed methodology used a widely recognized Harten Lax-Leer (HLL) solver for flux calculation. The suggested finite volume technique is a well-balanced, conservative, non-oscillatory approach ideal for computing the flow depth in various flow regimes of shallow water equations. The developed finite volume model dealt with the steady state of still water in a lake at rest. In addition, the model was validated by applying it to several benchmark tests. The results showed a high concurrence with analytical solutions based on the statistical tests. For the subcritical condition, the standard deviation was 5.73E-03, the root mean square error was 5.84E-03, and the coefficient of determination was 0.9994. For the supercritical condition, the standard deviation was 3.3E-02, the root mean square error was 3.334E-02, and the coefficient of determination was 0.998.Furthermore, the suggested model effectively simulatesthe Hishkaro River's flow during the flood season.