Conservation Properties of Unsteady Open Channel Flow Equations

Simulation of unsteady flow in open channels has always been of great interest to the hydraulic engineers. The Saint-Venant equations are usually used for this purpose. The 1-D version of these equations can be written in six different forms by choosing various dependent variables. After clarifying the notion of conservation versus non-conservation forms of these equation sets, the nature of flux vector based on conservation form and the eigenstructure property of Jacobian matrix of flux vector based on non-conservation form are explained in some detail. Shortcomings pertaining to earlier experimental design to confirm the conservation properties of various forms are documented and the role of consistent initial and internal boundary conditions across the discontinuity is highlighted. It is shown that the conservation properties of various forms cannot be uncovered by resorting to non-conservation forms of each equation set. It is recommended that the governing equations be written in conservation form in order to capture the discontinuity under consideration and let the program itself decide which property has to be conserved.

Keywords:

Saint-Venant , Conservation , Momentum , Energy