Comparative Study of Finite Difference Schemes for Discontinuous Flow Analysis in Open Channels

Abstract

Some numerical aspects of the upwind TVD scheme, the 2 step Lax-Wendroff scheme and the Preissmann scheme are discussed for discontinuous flow analysis in open channels. The TV-stability analysis indicates that the 2 step Lax-Wendroff scheme has no TV-stability, and the Preissmann scheme has a bounded stable range with an upper and a lower limit derived from the TV-stability theory. Numerical experiments show that the upwind TVD scheme needs larger computational effort than conventional difference schemes, however, it is quite accurate and does not generate spurious oscillations close to discontinuous points. Furthermore, the 2 step Lax-Wendroff scheme cannot suppress numerical oscillations for discontinuous flow analysis; it is hard to apply the Preissmann scheme to the numerical analysis of flows including subcritical and supercritical flows.