Author(s): Hidekazu Yoshioka; Nobuhiko Kinjo; Koichi Unami; Masayuki Fujihara
Linked Author(s): Koichi Unami, Masayuki Fujihara
Keywords: Longitudinal dispersion phenomena; Locally one-dimensional open channel network; Advection-dispersion-decay equation; Conforming Petrov-Galerkin finite element scheme; Implicit internal boundary condition
Abstract: Analysis of longitudinal dispersion phenomena in turbulent open channel flows are ultimately reduced to tracking the paths of solute particles behaving as stochastic processes. This study develops an efficient numerical model for the longitudinal dispersion phenomena in open channel networks. The path of each solute particle is taken as a continuous stochastic process governed by an Ito’s stochastic differential equation on a locally one-dimensional open channel network. An advection-dispersion-decay equation with a source term for cross-sectionally averaged solute concentration is deduced from an extended Kolmogorov forward equation associated to the stochastic differential equation. The advection-dispersion-decay equation is formulated as a weak form so that the junctions are consistently dealt with as implicit internal boundary conditions. A conforming Petrov-Galerkin finite element scheme for parabolic problems on locally one-dimensional open channel networks is applied to numerically solving the advection-dispersion-decay equation. Main novelty of the numerical scheme is the use of analytical solutions to local two-point boundary value problems in spatial discretization, which contributes to both stability and conservative property. Source term upwinding is successfully achieved using exponential weight functions. Temporal integration of the numerical scheme is carried out with a local θ-method in conjunction with a selective lumping algorithm in order to reduce numerical diffusivity and to obtain positivity preserving numerical solutions. A number of test problems, some of which are nonlinear and exhibit sharp contrasts in dispersivity and decay coefficient, are examined to determine accuracy of the numerical scheme. The numerical solutions satisfy positivity and conserve solute mass. Finally, numerical simulation of water quality dynamics in an agricultural drainage system is carried out to demonstrate versatility of the proposed model.
Year: 2013