Adapted MacCormack Finite-Differences Scheme for Water Hammer Simulation

Abstract

An adapted second-order accurate MacCormack finite-differences scheme is introduced and tested for the integration of the water hammer equations for a friction pipe. A fractional method is used to solve the governing equations in two steps with the Runge-Kutta splitting technique. The details of the proposed improvement technique, boundary condition inclusion and the shock capturing capability are presented in this paper. The numerical oscillations resulting from the dispersive errors of the MacCormack original scheme are treated using the artificial viscosity procedure. The results computed using the adapted MacCormack scheme for a friction pipeline with the original scheme with numerical viscosity are compared and analyzed. It is shown that for an abrupt varied flow, the proposed technique leads to better results.