Impact of momentum correction coefficient on simulating steady open channel flows

When simulating floods with the shallow water equations, the traditional Alternating Direction Implicit (ADI) scheme has proved to be incapable of modelling trans-critical flows. Spurious oscillations tend to arise in the predicted solutions near the sharp variations of the free surfaces and flow speeds. However, this scheme is still being commonly used in many commercial software. The modification of the momentum correction coefficient is one of the widely-used numerical treatments which allows the ADI scheme to produce seemingly-reasonable results. In this study, such a numerical treatment is examined by modelling the one-dimensional steady flow over an irregular bed and a two-dimensional flood in Boscastle, UK. The shock-capturing TVD-MacCormack prediction is used as reference in the test cases. The findings in this paper suggest that the decrease of the momentum correction coefficient helps reduce the amplitude of the numerical oscillations generated by the ADI scheme. Meanwhile, the predicted water surface elevation is underestimated with a reduced momentum correction coefficient. These results are useful for evaluating the accuracy of ADI simulations when being applied to trans-critical flow