Particle method of characteristics (PMOC) for unsteady pipe flow

A novel particle method of characteristics (PMOC) to simulate unsteady pipe flows is introduced and validated in the present study. Contrary to the conventional method of characteristics (MOC), the present formulation is built by reallocating the computational nodes along the characteristic lines. Both the right- and left-running characteristics are accurately traced and imitated with their associated computational particles. The annoying numerical inconveniences in the fixed-grid arrangement due to incompatible Courant–Friedrichs–Lewy (CFL) condition by repeating solution interpolations is effectively eliminated. Special particles with dual states satisfying the Rankine–Hugoniot relations are deliberately imposed to emulate the shock structure. Efficacy of this formulation is verified by solving some benchmark problems with significant transient effects in pipe flows. Computational results of piezometric head and flow velocity are meticulously compared with available analytical solutions. It is concluded that the proposed PMOC will be a useful tool to replicate transient phenomena in pipe flows.

[1]  R. LeVeque.  Finite Volume Methods for Hyperbolic Problems: Characteristics and Riemann Problems for Linear Hyperbolic Equations , 2002 .

[2]  J. Monaghan,et al.  Smoothed particle hydrodynamics: Theory and application to non-spherical stars , 1977 .

[3]  R. E. Ferguson,et al.  A COMPUTER PROGRAM FOR THE NUMERICAL SOLUTION OF HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS BY THE METHOD OF CHARACTERISTICS , 1968 .

[4]  R. Harrop.  An Introduction to the Method of Characteristics , 1953 .

[5]  E. Benjamin Wylie,et al.  Fluid Transients in Systems , 1993 .

[6]  I. A. Sibetheros,et al.  Spline Interpolations for Water Hammer Analysis , 1987 .

[7]  Yao-Hsin Hwang,et al.  A Moving Particle Method with Embedded Pressure Mesh (MPPM) for Incompressible Flow Calculations , 2011 .

[8]  Y. Hwang,et al.  A fast Godunov method for the water‐hammer problem , 2002 .

[9]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme I. The quest of monotonicity , 1973 .

[11]  B. Karney,et al.  Equivalent Differential Equations in Fixed‐Grid Characteristics Method , 1994 .

[12]  Jinn-Chuang Yang,et al.  On the use of the reach-back characteristics method for calculation of dispersion , 1991 .

[13]  Hanif M. Chaudhry,et al.  Applied Hydraulic Transients , 1979 .

[14]  Mohamed Salah Ghidaoui,et al.  A Review of Water Hammer Theory and Practice , 2005 .

[15]  Mark J. Sundquist,et al.  Fixed-Grid Characteristics for Pipeline Transients , 1977 .

[16]  R. J. Sobey.  Analytical solutions for unsteady pipe flow , 2004 .

[17]  E. Wylie,et al.  Characteristics Method Using Time‐Line Interpolations , 1983 .