Comparing the trajectories of Shockwaves and rarefaction waves from CFD and Saint-Venant models during dambreak events

摘要

The computation of the celerity of Shockwaves and rarefaction waves following a dam-break event is very relevant and demand adequate numerical tools. CFD models have been used in dambreak analysis, and are particularly adequate when complex geometries are involved. Shallow-water based models are also very popular for the simulation of these flows, particularly when the equations are solved with approximate Riemann solvers. To our knowledge, there has been no systematic comparison between the celerities of the Shockwaves and rarefaction waves obtained from CFD and Saint-Venant models. This work presents a comparison between a two-dimensional, VOF model constructed with OpenFOAM, and simulation results from one-dimensional, finite volume flow solvers using various numerical schemes (LxW, Roe, HLL). By neglecting source terms in the Saint-Venant formulation, analytical solutions for these celerities have also been derived. A comparison between the celerities from CFD, Saint-Venant and analytical results is presented for various ideal dambreak scenarios (dry bed and three depth ratios). Tracking of shock and rarefaction wave in CFD was made through monitoring the moment when pressures changed past a certain threshold. Results indicated that Saint-Venant results are, as expected, generally very close to analytical solutions. CFD results will be similar to analytical solution when the pressure threshold is set to very small value, e.g. 1%, of variation from the initial pressure of the bottom cell. Such findings can be useful in interpreting results obtained with these different solution approaches for calculation of wave celerities in dambreak events.