A fully conservative Beam and Warming scheme for transient open channel flows

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Abstract
A fully conservative Beam and Warming scheme that uses Roe's approximate Jacobian is presented for solving transient open channel flows. A general treatment for satisfying entropy inequality condition is incorporated which always leads to a physically realistic solution. Details of the Beam and Warming scheme, inclusion of the source terms and proposed modifications for achieving full conservation are presented. Improvement in accuracy achieved with the proposed treatment is demonstrated by comparing numerical results by different versions of the scheme with analytical solutions. The applicability of the scheme is examined by comparing numerical results with experimental data and numerical results from existing studies. The scheme's response (o the Courant number and Manning's coefficient is also investigated.