Finite-Element Model for High-Velocity Channels

Numerical modelers of high-velocity channels are faced with supercritical transitions and the difficulty in capturing discontinuities in the flow field, known as hydraulic jumps. The implied smoothness of a numerical scheme can produce fictitious oscillations near these jump locations and can lead to instability. It is also important that the discrete numerical operations preserve the Rankine-Hugoniot conditions and accurately model jump speed and location. The geometric complexity of high-velocity channels with bridge piers and service ramps are easily represented using an unstructured model. A two-dimensional finite-element model that utilizes a characteristic based Petrov-Galerkin method and a shock-detection mechanism, which relies on elemental energy variation results in a robust system to model high-velocity channels. Comparisons are made between analytic shock-speed results, published laboratory data of a lateral contraction, and with a more general physical model.