Flow and dispersion analysis of shallow water problems with Froude number variation

A shallow water flow model and a pollutant transport model were developed, and this study highlighted the practical applications of the coupled flow and dispersion models in terms of general properties. The flow model used the Petrov–Galerkin method in which the test functions are deformed by the current direction to introduce balancing diffusion only in the flow direction. The developed flow model was coupled to the pollutant transport model with a spatially varied dispersion tensor to demonstrate soluble constituent mixing. Three applications were considered to test the model performance under various Fr numbers. In the first application, the flow passing through a flume with an abrupt sidewall expansion was considered, and the model prediction was verified by experimental values, focusing on recirculation and the pollutant cloud trap. In the second and the third applications, the trans-critical and super-critical flow regimes evolved in non-uniform channels with an expanding or converging sidewall were reproduced, and pollutant mixing by a spatially varied dispersion tensor was investigated.