This paper reports a numerical computation for a reach of the Madeira River, a tributary of the Amazon, with aim to develop two general-purpose computational codes for grid generation (grid-generator) and flow/pollutant transport (flow-solver) in the complex domains of natural rivers. The adopted quasi-3D hydrodynamic model is closed by turbulence depth-integrated k̃ - ε̃ and k̃ - w̃ models. The advanced SIMPLE (Semi-Implicit Method for Pressure-Linked Equation) algorithm for FVA (Finite Volume Approach), ILU (Incomplete Lower-Upper) decomposition, PWIM (Pressure Weighting Interpolation Method), SIP (Strongly Implicit Procedure), under relaxation and multi-grid iterative method have been used to solve the hydrodynamic fundamental equations, discretized on non-orthogonal boundary-fitted grid with collocated variable arrangement. The results, calculated by different turbulence two-equation closure models, have been compared and discussed. Except for steady flow simulations, the processes of pollutant inpouring and plume development at the beginning of side discharge have been also investigated. 727731China Society for Hydropower Engineering,Chinese Hydraulic Engineering Society,et al.,Int. Assoc. Hydraulic Eng. Res. (IAHR),National Natural Science Foundation of China,State Key Lab. Hydrology-Water Resources Hydraulic Eng.Liren, Y., Nnb, S., Modeling water quality in rivers (2005) American Journal of Applied Sciences, 2 (4), pp. 881-886Liren, Y., Righetto, A.M., Tidal and transport modelling by using turbulence k̃ - W̃ model (1998) Journal of Environmental Engineering (ASCE), 124 (3), pp. 212-221Liren, Y., Righetto, A.M., Depth-averaged turbulence k̃-w̃ model and applications (2001) Advances in Engineering Software, 32 (5), pp. 375-394Peric, M., Kessler, R., Scheuerer, G., Comparison of finite-volume numerical methods with staggered and collocated grids, comput (1988) Fluid, 16, pp. 389-403Liren, Y., Righetto, A.M., Modelos de turbulência e aplicações a corpos D'Água naturais (1999) Métodos Numéricos Em Recursos Hídricos, 4, pp. 1-122. , Editor: Rui Carlos Vieira da Silva, Brazilian Association of Water Resources (ABRH), Chapter IMcguirk, J.J., Rodi, W., (1977) A Depth-averaged Mathematical Model for Side Discharges into Open Channel Flow, SFB 80/T/88, , Universität KarlsruheLiren, Y., Shunong, Z., A new depth-averaged two-equation (k̃ - W̃) turbulent closure model (1989) Journal of Hydrodynamics, 1 (3)