Numerical-experimental contrast of a mathematical model that simulates the movement of a fluid under shallow water conditions including energy losses

Abstract

In this paper, a comparison between the results obtained in laboratory experiments and those calculated by a numerical simulation of shallow water equations in an open channel is performed, considering the energy losses that occur as it passes through a local narrowing of the cross section. The mathematical model that simulates this physical phenomenon is governed by a partial differential equations system whose solution provides the water depth and the flow rate per unit of width, which is related to the velocity of the water. Such movement is controlled primarily by the force of gravity, being fundamental the relationship between it and the inertial forces. In the present study we have also taken into account energy losses caused by friction of the water with the contours and local losses caused by obstacles or changes in the width of the channel. A numerical scheme based on a high-order finite volume method has been used for obtaining the solutions of such model. Two type of laboratory tests have been simulated. The first type represents a slow transition regime, upstream and downstream of a narrowing in the channel. The second type represents a subcritical flow upstream, a narrowing that works as a control (regime change) and a downstream supercritical flow. Numerical-experimental comparison demonstrates the importance of adequately modeling of the different physical phenomena involved in the process, and the proper imposition of the boundary conditions of the problem.

Keywords

• Modelo matemático
• contraste numérico-experimental
• ecuaciones de aguas someras
• pérdidas de energía