ENERGY ESTIMATES FOR DISCRETIZATION ERRORS IN WATER-HAMMER PROBLEMS

An integrated energy approach is developed for transient problems in p ipelines using the fixed-grid method of characteristics. The goal is t o understand how discretization errors associated with common interpol ation schemes arise and how these errors can be controlled. Specifical ly, new analytical energy expressions demonstrate that both time-line and space-line interpolation attenuate the total energy of the system; in contrast, the wave-speed adjustment approach preserves the total e nergy but distorts the partitioning between kinetic and internal energ y. The analytic results are confirmed through numerical studies of sev eral series pipe systems. Both the numerical experiments and the mathe matical expressions show that the discretization errors are small and can be ignored as long as the work in the system is continuous and sub stantial. When the work is small or negligible, however, a Courant num ber C, value close to 1 is required to control the numerical dissipati on.