A TVD-WAF finite volume model for roll wave simulation

Roll waves appear as successive transitions from super- to sub-critical flows by passing through moving hydraulic jumps. Such discontinuous periodic waves propagate in a staircase pattern at constant wave celerity. On the basis of nonlinear shallow water (NLSW) equations, a finite volume model is presented to study the evolution of roll waves in inclined steep channels. The numerical model exploits the total variation diminishing version of weighted average flux (TVD-WAF) explicit method to solve the homogeneous NLSW equations. An implicit trapezoidal time integration operator is implemented for the treatment of source term which includes contributions from both the channel slope and frictional resistance. The simulated surface profile and flow velocity are in well agreement with available analytical solution for roll waves. The time evolution of wave amplitude under different undisturbed Froude numbers are investigated numerically and compared with theoretical predictions. Temporal decay of initial disturbance is discussed in which case roll waves no longer form. The observed agreement implies the efficiency and accuracy of the present scheme for roll wave modeling.