Effect of convective term suppression in numerical simulation of trans-critical open channel flow

Abstract

The implementation of boundary conditions in sub-critical and supercritical flow is quite different when using characteristics leading to programming difficulties with the associated numerical schemes. For supercritical flow, the de Saint Venant equations require two upstream boundary conditions and no downstream condition, whereas sub-critical flow requires one upstream and one downstream condition. The literature contains many approaches to accommodate both super- and sub-critical flows. Reducing or suppressing the convective term is one of the common methods which allows the same numerical scheme to be used for both regimes. In this paper, the impact of suppressing the convective term on the solution is investigated using the Method of Characteristics (MOC). A set of numerical experiments are carried out for this purpose using the commercial software MIKE11, and the results are compared and contrasted with MOC. Results show that significant changes in computed water depths occur in some situations by suppressing the convective term. In conclusion, in some cases the solution algorithm is significantly affected by this approximation. Also, since recent advances in numerical modeling of trans-critical flow are superior, this approximation should gradually be removed from the numerical simulation of open channel flow.