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Boundary condition treatment in 2×2 systems of propagation equations

✍ Scribed by Vincent Guinot

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
183 KB
Volume
42
Category
Article
ISSN
0029-5981

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✦ Synopsis

Numerical modelling of the water hammer phenomenon involves solving a 2;2 system of propagation equations numerically. In the present paper, this system is solved using the Piecewise Parabolic Method (PPM) Scheme, a higher-order extension of the Godunov Method. To reach high-order discretization accuracy, the PPM scheme uses six points in space to solve the advection equation. Hence, treatment of boundary conditions-which proves to be of importance to water hammer modelling-is not straightforward. Several options for the handling of boundary conditions are presented herein, and only one combination among nine is shown to provide good results. This shows that even very accurate numerical schemes may be of poor help in problem solving if boundary conditions are not handled properly. Results given by the PPM scheme are compared with those given by other solution techniques (Method Of Characteristics-MOC), proving the superior accuracy-efficiency relations used by the PPM over the usual approximations of the MOC.

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