Second order scheme for open channel flow

Abstract

In the search for a numerical scheme which: (i) is semi-descrete in nature (only space discritization) so that built-in ODE solvers in MATLAB or Modelica can be used, (ii) can handle dry bed conditions (island or dry shoals), (iii) is Reimenn-solver free so that it can be used as a black box solver, (iv) is higher order yet Total Variation Diminishing (TVD), (v) can handle bed discontinuities (discontinuity in bottom topography), (vi) can handle width discontinuities, (vii) is well-balanced and preserves the static equilibria (lake-at- rest), and (viii) can be modi ed to support higher order polynomial reconstruction, a second order accurate scheme known as Kurganov-Petrova central upwind scheme is presented. The scheme is implemented in MATLAB and a case study of a run-of-river power plant is described.