Simulation of hydraulic jump with grid adaptation

Abstract

In a hydraulic jump, the supercritical flow suddenly changes to subcritical flow forming steep gradients of flow depth and velocity. In the numerical simulation of this flow, proper grid distribution can play a crucial role in the prediction and resolution of the solutions. In this paper, two different numerical schemes - Mac- Cormack (second-order accurate in space and time) and two-four (fourth-order accurate in space and secondorder accurate in time) -are used with grid adaptation to numerically simulate the hydraulic jump at different Froude numbers in a rectangular channel. Rai and Anderson's method is used to determine the grid speed; however, a different partial differential equation based on the conservative principle of grid arc lengths for clustering the grid points in one-dimensional flow is used along with the Boussinesq equations to simulate the flow.

A number of tests were conducted at different Froude numbers tot confirm published data. The numerical results of the flow solutions are presented and compared with the experimental data and with numerical results without adaptation. The grid adaptation improved the flow solutions and the resolution; however, the order of accuracy of the schemes higher than second-order is found to have little effect on the solutions when solved under identical initial and boundary conditions. In addition, the importance of the Boussinesq terms in the governing equation is discussed and their effects on the flow solutions are investigated.