Numerical Oscillations in Pipe-filling Bore Predictions by Shock-Capturing Models

The introduction of non-linear, shock-capturing schemes has improved numerical predictions of hydraulic bores but significant numerical oscillations have been reported in the predictions of pipe-filling bore fronts associated with the transition between open-channel and pressurized flow regimes. These oscillations can compromise the stability of numerical models. A study of these oscillations indicates that the strength of the numerical oscillations is associated with the sharp discontinuities in the flow parameters across the jump, particularly the wave celerity. Approaches to attenuate oscillations by artificially reducing acoustic wave speeds may result in the loss of simulation accuracy. Two new techniques to attenuate the oscillation amplitudes are presented, the first based on numerical filtering of the oscillations and the second based on a new flux function that judiciously introduces numerical diffusion only in the vicinity of the bore front. Both approaches are effective in decreasing the strength of the numerical oscillations.