Numerical Simulation of Supercritical Flow at Abrupt Expansion Channel Using a Two-Dimensional Shallow Water Model

High-velocity flow is commonly associated with higher energy and any abrupt changes in the flow direction will involve high impact force. This phenomenon is often accompanied by the formation of shock wave and hydraulic jump in the downstream flow region. If the cross section in the expansion structure changes too rapidly, the flow might fail to be confined within the channel. The shock wave tends to overtop the sidewall and causing damage to hydraulic structure and its surrounding environment. In this study, the authors developed a two-dimensional numerical model based on the shallow water equation, based on the Cartesian staggered grid system. The advection terms are solved by the Constrained Interpolation Profile (CIP) scheme, while the non-advection terms are solved implicitly by using the SMAC method. To investigate the accuracy and stability of the numerical model, verification procedures was conducted by simulating the one-dimensional idealised dam break flow problem over the dry bed and wet bed. the performances of the numerical model is also compared against the simulation of two-dimensional partial dam break flow problem. A physical model is set up to reproduce the phenomenon of high-velocity flow at the abrupt expansion channel. Supercritical flow is introduced into an abruptly expanded tail water channel. The two-dimensional shallow water model developed is used to simulate the event of high-velocity flow at the sudden expansion channel based on the experimental conditions. The numerical model is capable to reproduce the flow features (i.e. the zone of constant depth and velocity, demarcation line and shock wave) occurred with the high-velocity flow at the abrupt expansion channel. The authors compared the numerical results with the analytical solution from literature studies and experimental work. In addition, the performances of the numerical model is compared against a numerical model with lower order of accuracy, i.e. a FLOW-3D model is set up under the same numerical conditions for this purpose.