Abstract
The finite element method is applied to the solution of a transient problem in a closed pipeline system. For primary investigations, however, considerations are restricted to the problem of a single pipeline system although the method, inherently versatile, is well suited for problems involving complex interconnected networks. Based on the non-simplified equations with lesser important terms, two different explicit finite element models, aided by the Kawachi scheme and the two-step Lax-Wendroff scheme for time marching, are built, including the selective consistency (or lumping) technique in the approximation of the time derivatives. Both frictionless and frictional waterhammer problems in the infinitely stiff pipe are practically solved by operating the two models developed, to examine their validities and compare their basic features. Accuracy of the solutions obtained is then estimated referring to the well-defined exact and non-interpolated characteristics solutions. It is demonstrated through those numerical experiments that in both models numerical dissipation as well as computational stability depend importantly upon the degree of consistency in time advance, and that especially the model combined with the Kawachi scheme has an advantage of being stable for time increment exceeding that allowable in the commonly used explicit schemes.
