Development of Reasonable Numerical Methods For Predicting Complicated Hydraulic Appearance With Different Time and Space Scales

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(1)The numerical methods are discussed theoretically and experimentally developed for predicting water surface of one dimensionally varied steady flows in open channels with a regular cross-section and locally varied resistance zone near the one-sided wall. The resistance zone is composed of pile series arranged like vegetation belt or rough stone zone. The lateral distribution of depth-averaged velocity within a cross section is firstly estimated from the equation of motion including the eddy diffusion effects due to interaction between distributed piles. The longitudinal water level is calculated using the one-dimensional energy equation in which the resistance effect of the pile zone is estimated as the lateral velocity distribution. The comparisons between the experimental and calculated values with respect to the velocities and water levels are very good to examine the usefulness of the analyses. The similar method is extended to the channels with compound sections. With that meth … More od, the cross sections of the flow were divided into three regions to predict the distribution of velocity and water level. With the previous methods the lateral velocity distribution assumes the uniform flow condition while we assume non-uniform flows. The longitudinal water level can be predicted by using the lateral velocity distribution and the energy slope obtained from that velocity distribution. The calculation method is validated by comparisons of the results obtained from the experiments made in the channels with regular and compound sections under the conditions of several kinds of pile zones.(2) To design reasonably grids for slow and rapid transient analysis using the method of characteristics is required to estimate the errors due to the discretizations and lime-line interpolations. The discretization errors for the linear valve closure problems in the simple piping systems is numerically and theoretically investigated with respect to pressure head rises, and formulated as the non-dimensional semi-theoretic equation, which is a function of the time scale of waves(valve closure time), pipe length, wavespeeds, number of pipes, and frictional coefficients. The combined time-line method for slow and rapid transient analysis is offered through designing adequate time-step sizes and grids, which satisfy the criteria for the discretization error and the error du to time-line interpolations. It is examined by numerical computations of transients using the pipeline model. Less