A 2D local discontinuous Galerkin method for contaminant transport in channel bends

Abstract

In this work, a third-order local discontinuous Galerkin (LDG) method is applied to the numerical integration of a two-dimensional, depth-integrated mathematical model describing the flow hydrodynamics and the transport of a passive contaminant in open-channel bends.The mathematical model is described in Begnudelli et al. (2010) [14] and treats the main physical aspects of the flow in curved channels (including bottom shear, momentum dispersion, scalar dispersion and turbulent diffusion) with a homogeneous degree of complexity and exhaustiveness. The numerical integration is performed using the scheme presented in Caleffi and Valiani (2012) [27], which is extended in this work to allow the treatment of diffusion terms. The capability of the model to correctly and efficiently treat computational domains with curved boundaries while preserving the exact well-balancing property is of fundamental importance for the correct simulation of the free-surface flow in laboratory flumes and real channels.Three test cases are used to validate the model. The first case consists of a problem, with an analytical solution, related to the tracer convection–diffusion in a uniform flow. This test is selected to highlight the excellent resolution obtainable using an LDG method. The other test cases, consisting of comparisons between numerical results and laboratory data, are selected to verify the capability of the model to reproduce real world phenomena. Both steady and unsteady tracer dispersion are taken into account.The results show the potentiality of the high-order accuracy models when applied to engineering problems that are characterized by inherently complex physical phenomena. The results also confirm the possibility of using extremely coarse grids, which leads to a high computational efficiency, in these real-world applications. Moreover, the good agreement between the experiments and simulations is a further confirmation of the suitability of two-dimensional depth-averaged models for the study of the convection–dispersion of momentum and pollutants in curved channels and rivers.Finally, the reconstruction of the solution by polynomial shape functions, which are typical of the LDG schemes, allows the streamline curvature, which is necessary to evaluate the diffusion coefficients, to be computed in a self-consistent manner, without the use of arbitrary reconstructions.