Two-layer shallow water formula with slope and uneven bottom solved by finite volume method

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 22 آذر 1401  

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2022.79205.1190

نویسندگان

Ummu Habibah ¹؛ Ismi Rizqa Lina²؛ Wuryansari Muharini Kusumawinahyu¹

¹Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang, Indonesia.

²Department of Data Science, University of Insan Cita Indonesia, Jakarta, Indonesia.

چکیده

This paper proposes a numerical approach to solve a two-layer shallow water formula with a slope and uneven bottom.  The Finite Volume Method (FVM) is applied to solve the shallow water model because the method is suitable for Computational Fluid Dynamics (CFD) problem. Rather than pointwise approximations at grid points, the FVM breaks the domain into grid cells and approximates the total integral over grid cells. The shallow water model is examined in two cases, the shallow water model in the steady state and the unsteady state. The Quadratic Upstream Interpolation for Convective Kinetics (QUICK) is chosen to get the discretization of the space domain since it is a third-order scheme that provides good accuracy and this scheme has been proven numerical stablity. The advantage of QUICK  method is that the main coefficients are positive and satisfy the requirements for conservativeness, boundedness, and transportiveness. An explicit scheme is used to get the discretization of the time domain. Finally, the numerical solution of the steady state model shows that the flow remains unchanged. An unsteady-state numerical solution produces instability (wavy at the bottom layer). Moreover, the larger slope results in higher velocity and higher depth at the second layer.

کلیدواژه‌ها

Two-layer shallow water؛ Finite Volume Method؛ QUICK scheme؛ Explicit scheme