A new finite volume method on junction coupling and boundary treatment for flow network system analyses

Abstract

To adequately analyze the flow in a pipe or duct network system, traditional node-based junction coupling methods require junction losses, which are specified by empirical or analytic correlations. In this paper, a new finite volume junction coupling method using a ghost junction cell is developed by considering the interchange of linear momentum as well as the important wall effect at the junction without requiring any correlation on the junction loss. Also, boundary treatment is modified to preserve the stagnation enthalpy across boundaries, such as the pipe end and the interface between the junction and the branch. The computational accuracy and efficiency of Godunov-type finite volume schemes are investigated by tracing the total mechanical energy of rapid transients due to sudden closure of a valve at the downstream end. Among the approximate Riemann solvers, the proposed RoeM scheme turns out to be more suitable for finite volume junction treatment than the original Roe's approximate Riemann solver because of conservation of the stagnation enthalpy across the geometric discontinuity. From the viewpoint of computational cost, the implicit LU-SGS time integration is appropriate for steady and slow transients, while the explicit third-order TVD Runge-Kutta scheme is advantageous for rapid transients. Copyright (C) 2009 John Wiley Sons, Ltd.