A method to calculate inverse solutions for steady open channel free-surface flow

Abstract

The inverse problem of steady two-dimensional open channel free-surface flow is considered, with the focus on determining two types of disturbances: a surface pressure distribution and solid channel bottom topography. A closed-form expression for the inverse surface pressure is derived, and a linear Fredholm equation of the first kind is shown to describe the inverse topography problem, which then needs to be descretised and solved numerically. However, the equation for the channel bottom is prone to instability, so the truncated singular value decomposition (TSVD) method is proposed as a way to stabilise the associated discrete solution. The effectiveness of the TSVD method is demonstrated through several numerical examples, and its performance in the presence of error-contaminated input data is also examined. The results show that the TSVD method can recover the topography accurately from the forward free-surface problem, and provide good approximations even with noisy input data.