A New Conservative Form of the 1D Saint Venant Equations and Its Numerical Solutions

The 1D Saint Venant equations with water surface level as a primitive variable have flexibility for flows over irregular geometries. However, the primitive variable of water surface level changes the Saint Venant equations into a non-conservative form. This paper proposes a new conservative form of 1D Saint Venant equations with water surface level as one of the primitive variables. A Godunov type numerical scheme with an improved HLL Riemann solver was implemented to solve the equations. Numerical solutions were compared with various experimental and theoretical test examples. It is shown that the proposed conservation form along with the improved HLL numerical scheme is capable of dealing with various open channel flows over complex geometries such as ideal dambreak flows with dry and wet bed, hydraulic jump, steady flows over bump, wave interactions, and partial dam-break flows across abrupt contraction of cross-section.