A generalized reconstruction technique for the approximate solution of discontinuous bed Shallow-water Equations

One-dimensional Shallow-water Equations are written considering, among the others, the hypotheses of hydrostatic pressure distribution and small bed slope: the system of hyperbolic equations which is obtained exhibits a geometric source term which is proportional to the nonconservative product of the water depth by the bed slope. Here, following the theory by Dal Maso, LeFloch and Murat, a numerical scheme is presented, which is well balanced and able to capture contact discontinuities due to bottom steps: the path used for the definition of the nonconservative product, able to represent the head losses encountered passing over the bottom discontinuity, is chosen in order to consider a hydrostatic pressure distribution acting onto the bed step