Implicit Bidiagonal Scheme for Depth-Averaged Free-Surface Flow Equations

Abstract

A general fast implicit bidiagonal numerical scheme, based on the MacCormack's predictor-corrector technique requiring the inversion of only block bidiagonal matrices, has been developed and subsequently applied for subcritical and supercritical free-surface flow calculations. The model has been applied to depth-averaged steady flows. There are two main advantages of the proposed method: the technique has fast convergence and utilizes a body fitted nonorthogonal local coordinate system to simulate irregular geometry flows. The model is used to analyze a wide variety of hydraulic engineering problems including flows in a converging-diverging subcritical flume, supercritical expansions at various Froude numbers, and supercritical converging chutes. For each of these test cases, the calculated results are compared with experimental data. The comparisons with measurements as well as with other numerical solutions show that the proposed method is comparatively accurate, fast, and reliable.