MODELING OF UNSTEADY RAPIDLY VARIED OPEN CHANNEL FLOW

摘要

The modeling of unsteady surface water flows such as roll waves, surges, tidal waves and floods and flow routing poses great challenge to numerical modelers. In this paper, three explicit schemes for unsteady surface water flows are investigated. The three schemes differ in the way by which the mass and momentum fluxes at the interface between different finite volumes are determined. In particular, the flux in the Bhatnagar-Gross-Krook (BGK), the kinetic flux vector splitting (KFVS) and the flux difference splitting (FDS) schemes are based on Boltzmann Bhathagar-Gross-Krook equation, the Boltzmann equation with no collision and the exact Riemann solution, respectively. The gravitational and frictional forces are included through operator splitting for all three schemes. Test cases show that (ⅰ) the three schemes accurately resolve shock waves, expansion waves and the nonlinear interaction between various waves, and (ⅱ) the three schemes are of similar accuracy and efficiency. However, it is noted that the scalar nature of the Boltzmann equation means that the BGK and KFVS do not require characteristic decomposition and that its extension to multi-dimensional problems or to flows in complex geometry is relatively straightforward.