Abstract
For two different finite element models previously developed for pipeline transient analysis, i.e., the first and second order models incorporating the Kawachi scheme and the two-step Lax-Wendroff scheme respectively, stability and accuracy analyses are performed to theoretically investigate how the consistency parameter as well as the common computational key factors affect the computational stability and the numerical dissipation and dispersion and to discuss the relative advantages of both schemes. The analyses demonstrate that in any case the Kawachi scheme, with the stability criterion: Courant number ≤2 in an extreme case, provides higher stability limit than the Lax-Wendroff scheme, and that both schemes with non-zero consistency parameter are dissipative attenuating useless high frequency wave components and then selective dissipativeness can be better achieved by the Lax-Wendroff scheme with a high level Courant number. In consequence, both models are qualified as of better suitability for an analysis of shock or steep-fronted wave like a waterhammer. Additionally, it is suggested that without any extra procedures, the Kawachi scheme can efficiently solve the variable wavespeed problems of air-water mixture when taking the benefit of being stable for a wider range of wavespeed variations.
