Comparison of Numerical Computation Schemes for One-dimensional Transition Flow

Abstract

In this paper, three different schemes, namely, Beam & Warming, Roe, and Lax-Wendroff schemes, are compared in numerical computation of one-dimensional open-channel unsteady free surface flows. Beam & Warming finite difference scheme is based on implicit scheme incorporated with flux vector splitting techniques, Roe and Lax-Wendroff finite difference schemes are based on explicit scheme with flux difference splitting techniques, and using approximate Jacobian in the model formulation. Flows with simultaneous presence of super critical and subcritical regions can be analyzed by the proposed models. Numerical examples are given and results obtained the computational schemes are compared with existing experiment data and analytical solutions, computer times and accuracy are presented to demonstrate applicability of the models for hydraulic studies involving rapidly vary flow. From this study, it may be concluded that Roe scheme based on flux splitting is preferable for practical applications.