Modeling Channel Bed Transients Using Explicit F‐D Schemes

Abstract

Nonlinearities of bed transients of finite height are documented through numerical modeling using finite difference schemes. First, the numerical characteristics of two explicit finite difference schemes, namely: de Vries's pseudoviscosity modified‐Lax and Fromm's zero‐average‐phase‐error schemes are presented. The performance of de Vries's scheme depends primarily on the relationship of the pseudoviscosity term to the bed Courant number selected and the spatial resolution used to discretize the bed wave, whereas the performance of Fromm's scheme depends on the bed Courant number chosen for the simulation. The optimal choice of these numerical parameters is a function of the bed wave height, the wave shape, and the Péclet and Froude numbers. These schemes are used in numerical simulations to determine the nonlinear behavior of a sinusoidal‐shaped bed transient of finite height. Comparing the simulated motion of the bed with that obtained by (linear small‐amplitude) analytical methods, correction factors for both effective bed wave celerity and attenuation are presented as functions of the dimensionless wave height, the Péclet and Froude numbers.