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Boundary condition treatment in 2×2 systems of propagation equations
Author(s) -
Guinot Vincent
Publication year - 1998
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19980630)42:4<647::aid-nme376>3.0.co;2-u
Subject(s) - discretization , mathematics , godunov's scheme , boundary (topology) , boundary value problem , piecewise , water hammer , scheme (mathematics) , numerical analysis , mathematical analysis , engineering , mechanical engineering
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. © 1998 John Wiley & Sons, Ltd.