Stochastic Solution to the Water Hammer Equations Using Polynomial Chaos Expansion with Random Boundary and Initial Conditions

摘要

In this paper, a stochastic method of characteristics (MOC) solver is developed based on polynomial chaos expansion (PCE) to quantify the uncertainty in water-hammer equations describing transient flow in a simple reservoir-pipeline-valve system. The randomness is considered due to boundary and initial conditions. The Galerkin scheme is used for the projection of equations onto the stochastic dimension, and the governing equations are solved for the expansion coefficients. These coefficients are then used to reconstruct the mean solution of pressure wave perturbation as a result of valve closure, in addition to the calculation of other higher-order statistical moments. The computed results are in excellent agreement with those calculated by using the traditional MOC over a wide range of system parameters including steady and unsteady friction. The stochastic solution has the advantage of being robust and more efficient than other nonintrusive methods, such as Monte Carlo simulations (MCS).