A conservative extension of the method of characteristics for 1-D shallow flows

The method of characteristics (MOC) has been used for a long time in open channels and pipes flows. It is based on non-conservative equations, and hence it cannot be used directly for solving discontinuous shallow flows. In this paper we develop a conservative version of the MOC scheme for 1-D shallow flows by imposing the conservation law at the interpolation step. The conservation property of the scheme ensures the production of an accurate shock modeling and enables the MOC scheme to simulate dam-break type flows. By using a proper interpolation function, the proposed method can also produce quite accurate low-oscillatory results. A number of challenging test cases show considerable improvement compared to the traditional non-conservative MOC scheme in the case of dam-break type and trans-critical flow simulations.