NUMERICAL-SIMULATION OF HYDRAULIC JUMP

Boussinesq equations describing one-dimensional unsteady, rapidly varied flows are integrated numerically to simulate both the sub- and supercritical flows and the formation of a hydraulic jump in a rectangular channel having a small bottom slope. For this purpose the MacCormack (second-order accurate in space and time) and two-four (second-order accurate in time and fourth-order in space) explicit finite-difference schemes are used to solve the governing equations subject to specified end conditions until a steady state is reached. The inclusion of initial and boundary conditions is discussed, and the importance of the Boussinesq terms is investigated. Complete test results for a range of Froude numbers are presented that may be used by other researchers for the verification of mathematical models. A comparison of the computed and measured results shows that the agreement between them is satisfactory for the fourth-order finite-difference scheme although the second-order scheme does not accurately predict the location of the jump. These simulations show that the Boussinesq terms have little effect in determining the location of the hydraulic jump.