Quasi-2D model for computation of supercritical free surface flow in sudden expansion

This work deals with the mathematical modeling of a supercritical flow at an abrupt channel expansion. A simplified approach for the study of the characteristics and features of the flow in the presence of the cross shock waves is then proposed. Based on the two-dimensional Saint-Venant equations and using certain simplifying assumptions in practice, this 2D shallow water model is reconverted to an equivalent 1D flow problem by inverting space time variables. The numerical solution of the 1D equation then makes it possible to reconstitute the solution of the 2D flow field according to translating planes. The results obtained show a satisfactory agreement with the experiments carried out for this problem. The profiles of the waterline along the wall and the flow axis are accurately reconstituted thus allowing the good design of the channel walls and the positioning of the oblique shock waves.