Accurate numerical modeling of 1D flow in channels with arbitrary shape. Application of the energy balanced property

This work focuses on the numerical treatment of 1D flow in channels with arbitrary shape using energy balanced arguments. The system of equations is defined using the mass and momentum conservation equations, allowing the resolution of hydraulic jumps where energy conservation arguments are not valid. When necessary, conservation of mechanical energy takes part actively in the numerical scheme when evaluating the source terms. The numerical scheme is based on an augmented Roe solver that involves the presence of source terms by adding an extra stationary wave. The characteristics of the numerical scheme include the energy balanced property, and being only first order accurate in time and space, leads to exact numerical solutions for steady solutions with independence of the grid refinement in channels with general geometries. Riemann problems considered here involve non-prismatic channels, bed variations and the resonance regime, including the limiting situation when the Riemann data belong to the resonance hypersurface. Numerical results point out that the finite volume numerical scheme with nonconservative terms presented here, converges to the exact solution. The well balanced property is ensured, as it is a particular case of the energy balanced property in cases of quiescent equilibrium.