River discharge estimation is critical in the implementation of flood management techniques, as well as essential flood defence and drainage systems. In the regular season, water only flows down the main channel; however, in the event of a flood, water exceeds the banks and reaches the floodplains, causing severe damage and loss of livelihood. The rivers consist of a main channel and floodplains, which together make up a compound channel during a flood. In non-prismatic compound channels where the floodplains are either diverging or converging longitudinally, calculating the discharge is a difficult task. Momentum transfer occurs at the interface of the main channel and floodplain in compound channels due to differences in flow velocity between subsections. It follows that in a non-prismatic compound channel, the flow behavior becomes extremely complex. The conveyance capacity of a channel is influenced by various flow factors, although three crucial ones are velocity distribution, bed shear stress, and secondary currents. However, due to the complexities of the methodology, prior experts have made very few attempts to compute the flow parameters for non-prismatic compound channels using numerical techniques. Thus, considering such difficulties, the current work uses subgroups of the k–ε and k–ω models to predict the flow properties for non-prismatic compound channels. The ANSYS-Fluent software package is used to carry out the computational fluid dynamics (CFD) simulations. There are four models that are used to mimic the diverging and converging non-prismatic compound channel: standard k–ε, RNG k–ε, standard k–ω and SST k–ω. Analysis is done on the velocity profiles and turbulent kinetic energy at four points across the channel and three points along its longitudinal direction. Comparing the present SST k–ω model to the other three turbulence models, the results are satisfactory. This study will be beneficial to hydraulic engineers and researchers working on compound channels.