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• The RBVMS formulation is a good option to model sediment transport in fluid flows. • The model developed has shown good agreement with the experimental data. • Upwind sand-slide is a robust method and the mass is preserved when it is applied. • Adaptive mesh refinement has shown to be important to save computational effort. Moving sediments are intrinsic to several engineering and natural phenomena. Consequently, the study of sediment transport induced by fluid flows is critical. The transport of sediments in fluids encompasses the suspended load and the bed-load. In the suspended load turbulence carries the sediment particles. The particles near the bottom are moved by sliding, rolling or by saltation, due to shear stresses in the bed-load region. The bed-load transport implies morphological changes which are also induced by erosion as a consequence of sediment entrainment into suspension. In this work, we implement these phenomena as numerical models for 2D simulations in libMesh, an open finite element library that provides a framework for multiphysics, considering adaptive mesh refinement. Here, the mathematical model results from the incompressible Navier–Stokes equations combined with an advection-diffusion transport equation for suspended sediments using an Arbitrary Lagrangian–Eulerian description. Both equations are treated with the residual-based variational multiscale finite element formulation. Empirical models are used to represent the entrainment and the bed-load transport rate of sediments. Special boundary conditions at the bottom are introduced to take into account sediment entrainment, as well as deposition. After each time step, we update the mesh according to the morphological changes at the bottom due the bed-load transport and erosion, considering smoothing techniques to avoid numerical instabilities. We also introduce a new smoothing technique, called upwind sand-slide, in which we consider the flow direction combined with the slope angle to avoid elevations higher than the sediment angle of repose. We validate the algorithm with test cases where experimental and numerical data are available. Finally, we discuss the results, concluding that our model is very promising. [ABSTRACT FROM AUTHOR]