MODIFIED TRANSFORMATION AND INTEGRATION OF 1D WAVE-EQUATIONS

This technical note introduces an alternative method of transforming h yperbolic partial-differential equations into characteristic form. The method is based on transforming the governing equations to a referenc e frame moving with finite speed u. Thus, the method is analogous to t he ''moving observers'' used traditionally in graphical water-hammer t heory to solve the equations of motion [e.g., Parmakian (1963) and Ber geron (1961)] or to the method of deriving simplified governing equati ons by using a translating reference frame [e.g., Henderson (1966)]. T he difference in the present case is that although the governing equat ions are assumed to be known, they are transformed into characteristic form by a shift in reference frame. Tn essence, the transformation us es the total derivative concept and is both simple and insightful. In fact, for both open-channel flow and water-hammer applications, it is shown that by transforming only the continuity equation along a charac teristic curve, the dynamic equation naturally arises during the trans formation. A mathematical justification and generalization of the prop osed method is provided.