Characteristics Method Using Time‐Line Interpolations

Abstract

The use of interpolations in time, rather than the more widely used spatial interpolations, demonstrates several benefits in the application of the method of characteristics to wave problems in hydraulics. Two such time‐line schemes are presented and analyzed in the solution of a linearized water hammer problem. Reachback time‐line interpolations, where the characteristic lines are projected back before the current time step, demonstrate less damping than the corresponding spatial interpolation scheme at the same discretization. Implicit time‐line interpolations, where the characteristic line is projected into the current time step, permit relaxation of the restrictive time step required by the Courant condition. An error analysis and numerical experiments demonstrate the degree of damping and dispersion introduced by both reachback and implicit time‐line interpolation methods. The error analyses and their verification may encourage further application of these methods in appropriate problem domains.