Second Order KP Scheme for the Solution of flow in a Venturi Channel

Abstract

In many different applications, a Venturi channel is used as a tool to compute fluid flow rates. The Saint-Venant equation is a hyperbolic type Partial Differential Equation (PDE) which can be used to model fluid flows through a Venturi channel. The suitability of the 2nd order Kurganov-Petrova (KP) scheme to solve the hyperbolic PDE for fluid flow in the Venturi channel is studied. A laboratory Venturi rig established at the University of South-Eastern Norway (USN) is used to measure the Steady State (SS) fluid levels along the channel. In this paper, the simulated results are compared with the experimental data. In addition, the simulation results obtained with the second order scheme for solving the Saint-Venant equations are compared with a 1st order numerical scheme. The Froude number for the flow is calculated to check the flow regime changes: from a subcritical flow to a supercritical flow in the Venturi section of the channel. The 2nd order KP scheme is found to be a suitable numerical scheme which can be used to discretize hyperbolic PDEs.

Second Order KP Scheme for the Solution of flow in a Venturi Channel