Modeling Unsteady Open‐Channel Flows—Modification to Beam and Warming Scheme

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Abstract
A modification to the well‐known Beam and Warming implicit scheme is proposed and is applied to one‐dimensional unsteady free‐surface flows. The proposed modification is based on the concept of conservative splitting of flux through an approximate Jacobian. The conservative evaluation of flux vector at known‐time level in the Beam and Warming scheme, hitherto evaluated nonconservatively, improves the accuracy of the solution and effectively eliminates mass balance error. Computational results of a number of illustrative examples are presented and compared with solutions of the original Beam and Warming scheme as well as with analytical solutions. The modified model significantly improves accuracy of results at almost no additional complication or cost of computation.

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