Turbidity currents occur widely in submarine environments, but field-scale numerical simulations of the flow features have not been applied extensively. Here, we present a two-dimensional layer-averaged numerical model to simulate turbidity currents over an erodible sediment bed, and taking into consideration deposition, entrainment and friction. The numerical model was developed based on the open-source code, Basilisk, ensuring well-balanced and positivity-preserving properties. An adaptive spatial discretization was used, which allows multi-level refinement. The adaptive criterion is based on the dynamic features of the flow and sediment concentrations. The numerical scheme has a relatively high computational efficiency compared with models based on the Cartesian mesh. A hypothetical case based on a true large-scale landform (the Moroccan Turbidite System, offshore NW Africa) was studied. Compared with previous models, the current model accounted for the coupling between flow, sediment transportation and bed evolution. This approach may improve simulation results and also allow the simulation of complex field-scale landforms, while preserving the flow details.