A diffusion wave finite element model for channel networks

Abstract

A computational algorithm for the solution of prismatic dendritic channel networks based on the diffusion wave approximation of channel flow is presented. Finite elements are used for the spatial approximation and an implicit linear time interpolation scheme is used for the temporal discretization of the diffusion wave equations. The implicit scheme results in a system of nonlinear algebraic equations, which are iteratively evaluated using successive substitution. This scheme does not require any system matrix updates of the symmetric and banded algebraic equations. A second iteration scheme is used to model the network junction point boundary conditions, which allows each channel segment to be independently discretized and evaluated.This approach significantly reduces the storage and matrix decomposition requirements in the solution of a channel network system. An adaptive time incrementation scheme, which strives to achieve constancy in the number of junction point boundary condition iterations, is presented. The model routes a specified set of hydrographs through the channel network, as well as any specified lateral inflow into the channel. Results are presented for an example of a dendritic network, using rectangular and trapezoidal channel geometries.