Space-Time Conservation Method Applied to Saint Venant Equations

Abstract
A new numerical technique by Chang is described and used to solve the one-dimensional (1D) and two-dimensional (2D) Saint Venant equations. This new technique differs from traditional numerical methods (i.e., finite-difference, finite-element, finite-volume, spectral methods, etc.). Chang's method treats space and time on the same footing, so that space and time are unified—a key characteristic that distinguishes the new method from other techniques. This method is explicit, uses a staggered grid, enforces flux conservation in space and time, and does not require upwinding, flux-splitting, flux limiters, evaluation of eigenvalues, or the addition of artificial viscosity. Furthermore, the scheme is simple, easy to implement (see Appendix I), and can be extended to higher dimensions. First, the new technique, as developed by Chang, is introduced, explained, and applied to the 1D Saint Venant equations. To illustrate its effectiveness, an idealized dam-break and a hydraulic jump in a straight rectangular cha...