Free surface flow over topography: an inverse approach

Abstract

The problem of steady two-dimensional open channel free surface ow over topography is studied. The focus here is on the inverse problem of recovering the pro le of the topography given prescribed surface data. This thesis explains the ill-posed nature of the inverse problem and develops a method based on the truncated singular value decomposition to obtain regularised inverse solutions for the topography given free surface data. It is shown how discretisation of the inverse problem yields a linear system to be solved and how regularisation can be applied to temper the ill-posed nature of the problem such that useful solutions can be obtained. This method is much less computationally expensive than previous approaches using the Newton method which enables a rapid exploration of the solution space. The developed method is trialled against input data from computed solutions to the forward problem to give a benchmark against which the performance of the model can be assessed, and it is found that it is able to accurately reconstruct the topography. We then show that the method can recover the topography even with substantial noise added to the surface. Finally we use the model to explore the solution space of the inverse problem.