Explicit central finite difference methods for fluid-structure interaction in liquid-filled pipe systems

Faeze Khalighi, Alireza Keramat, Ahmad Ahmadi

Thursday 2 july 2015

14:35 - 14:50h at Oceania (level 0)

Themes: (T) Water engineering, (ST) Computational methods

Parallel session: 12E. Engineering - Computational

Fluid-structure interaction (FSI) occurs when the dynamic water hammer forces, cause vibrations in the pipe wall. FSI in pipe systems being Poisson and junction coupling occurring due to water hammer has been the center of attention in recent years. It causes fluctuations in pressure heads and vibrations in the pipe wall. The governing equations of this phenomenon include a system of first order hyperbolic partial differential equations (PDEs). Historically, some methods such as Method of Characteristics (MOC) and Godunov's scheme have been successfully used for solving these equations but these methods suffer from restrictions on linearity of equations and space-time mesh sizing. This paper aims at the simulation of fluid-structure interaction in a reservoir-pipe-valve considering the Poisson and junction coupling. To this end a code written in Matlab based on explicit central finite difference methods is provided. The numerical scheme is appropriate for hyperbolic PDEs of this phenomenon. Two different numerical schemes are implemented: a two-step variant of the Lax-Friedrichs (LXF) method, and a method based on the Nessyahu-Tadmor (NT). The computational results are compared with the results of Method of characteristics, and also with the results of Godunov scheme to verify the proposed numerical solution. The LXF method is conservative and monotone; therefore, this is a total variation diminishing (TVD) method. The LXF scheme is based on a piecewise constant approximation of the solution like the original Godunov method, however it does not require solving a Riemann problem for time advancing and only uses flux estimates. Actually the prototype of Nessyahu-Tadmor method is LXF scheme. It's accuracy order is two and works with a staggered grid along with the reconstruction of MUSCL-type piecewise linear interpolants in space furthermore, oscillation-suppressing nonlinear limiters and midpoint quadrature rule for evaluating time integrals are adopted in the scheme. The results reveal that the proposed LXF and NT schemes can predict discontinuous with an acceptable order of accuracy. The independency of time and space steps allows for setting different grid size with a unique time step, thus increasing the accuracy with respect to the conventional MOC.