Internal Boundary Conditions for Solute Transport Equations in Locally One-dimensional Open Channel Networks

Abstract

  Transport phenomena of solute in open channel networks are described in the framework of longitudinal dispersion. Modeling of the longitudinal dispersion in an open channel network in general requires the use of a solute transport equation coupled with an internal boundary condition to appropriately determine the dynamics of solute concentration around junctions. However, only a few researches have focused on dependence of the longitudinal dispersion on the internal boundary conditions. This paper carries out theoretical and numerical analysis on two internal boundary conditions that have different physical and mathematical basis with each other. A conforming Petrov-Galerkin finite element scheme is used to solve the solute transport equation. Computational results of a series of numerical simulations reveal that the dynamics of the solute concentration in open channel networks critically depends on the internal boundary conditions in particular for the diffusion-dominant cases that arise in typical situations, indicating their importance in practical analysis.