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

Abstract

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.