Upwind Flux on Unstructured Finite Volume and Multi-Stage Computational Time Stepping for Simulation of Steady Shock Waves in Contracting Chutes

Document Type : Research Article



In order to adapt the hydraulic conditions of super critical flow in the chute spillways, variable width may be designed by designers. For most of the cases, the design of contracting chutes would help reducing water depth at upstream of the chute which reduces the dam height and increasing water depth at downstream of the chute may provide better smaller stilling basin for hydraulic jump. Super critical flow in the chute canals with contracting width may associate with the oblique steady shock waves. There are some difficulties in accurate numerical solution of water surface and velocity discontinuities due to shock waves. In this paper a novel algorithm for Overlapping-Cell-Vertex Unstructured-Finite- Volume solution of shallow water equations is used in which the numerical fluxes on the boundary edges of each Control-Volume are computed using an Upwind-Flux-Averaging formulation. Using this formulation in combination with Multi-Stage Runge-Kutta Time-Stepping provides accurate and oscillation free explicit solution of super critical flow with sharp shock waves. The accuracy of the computed result for analytical and experimental steady horizontal test cases is compared with reported data. The efficiency of the solution algorithm for the test cases is presented in terms of convergence history plots and CPU time consumption for the convergence of the solution to the steady state.