Testing Accuracy of Finite Element and Random Walk Schemes in Prediction of Pollutant Dispersion in Coastal Waters

Abstract

Distribution of pollutants in coastal waters is usually represented by depth averaged twodimensional convection-dispersion equation. Under very specific conditions this equation can be solved analytically. Although such a solution is restricted to simplified situations it provides a very useful case for testing the performance of various numerical solution techniques currently available for the simulation of convective-dispersion of pollutants in natural water systems. In this paper the analytical solution of the convective dispersion equation is used as a benchmark against which the accuracy of other techniques are assessed. These assessments are based on quantitative comparisons between the results of the solution of two-dimensional convection-dispersion equation by the deterministic finite element and stochastic random walk methods. Both Eulerian and Lagrangian frameworks are employed to obtain the finite element solution of the convection-dispersion problem. It has been shown that the Lagrange-Galerkin finite element scheme yields the most accurate results for the case under study. However, computational costs of the Lagrange-Galerkin method can be relatively high and under certain conditions it may be reasonable to use a less accurate but cost effective random walk scheme to make water quality management decisions.

Effects of Contaminant Decay on the Diffusion Centre of a River

“…Such exact solutions extend the scope for the benchmark testing [10] of numerical computation schemes for environmental impacts in rivers.…”

“…One motivation is to sharpen understanding. Another motive is to add decay examples to the stock of non-trivial exact solutions for the benchmark testing of numerical computation schemes for environmental impacts in rivers [10].…”

Numerical Modeling of Pollutant Dispersion and Oil Spreading by the Stochastic Discrete Particles Method

“…First we introduce a value of a characteristic time scale T corresponding to the physical process under consideration. It is naturally to choose the general diffusion coefficient K 0 such that the variances calculated in the models of turbulent and general diffusion coincide at time t = T. In accordance with (5) and (6) the unknown value of this effective coefficient is In the case of usual diffusion the pollutant plume near the source seems to be more scattered than that in the case of turbulent diffusion. In the latter case the pollutant surrounding the source is observed to have a greater concentration than in the first one.…”

“…In numerical simulations of these problems the statistical methods that consider an ensemble of walking discrete particles are often preferred in practice, e.g. [1][2][3][4][5].…”