Modelling of the flow structure change through a closed duct

Abstract

Free surface flow structure changes to pressurized in several cases. However, modelling this transition needs to consider the mathematical discontinuity. So, Riemann problem seems to be the adequate partial derivative system for describing this phenomenon. In this work, we used three numerical schemes to solve the mathematical model. The process time, the Courant number and the standard deviations values lead to deduce that the flux difference splitting, or Godunov scheme will be the most appropriate and