Shock-wave computations in channel contractions

Abstract

Commonly, depth-averaged Navier-Stokes equations are used for shock-wave computations. The classical approach is limited to regions where the hydrostatic pressure assumption is valid. An extended approach taking into account non-hydrostatic pressure distribution as well as momentum in the third direction improves the simulation of the complex wave pattern. A comparison between measurements, the classical and extended shallow water equations as well as with the fully three-dimensional Navier-Stokes equations is undertaken for computations of supercritical flow in a channel contraction considering Froude numbers 4 and 6. The results show that the limitations of the classical approach increase with the Froude number. The extended shallow water approach and the fully three-dimensional Navier-Stokes equations yield both a good agreement with the measurements.