Analytical and numerical solutions for sediment and heavy metal transport: a 1D simplified case

The use of mathematical models to study the transport of suspended sediments and heavy metals (HM) in water and riverbeds is of growing interest among the scientific community. A model of three partial differential equations solved by a numerical scheme of a third order was applied. The aim was to verify a numerical one-dimensional (1D) model for sediment and heavy metal concentrations in the water and bed applying analytical solutions, for three sedimentological conditions with a continuous source. The importance of the magnitude and sense of the diffusive process in the active bed sediment layer was studied. Differences between numerical and analytical results were quantified for: sediment concentration in the water column, total HM concentration in the water column and HM concentration in bed sediments. All these differences were less than 0.4% in all cases. Numerical results for two more complex scenarios were included. For the first scenario, water without HM flowing over a contaminated bed was assumed, whereas for the second one, the opposite - contaminated water with HM flowing over a clean bed - was adopted. A brief analysis of the initial conditions of HM concentration showed the importance of determining such initial conditions in actual environmental studies.