Abstract
An analytical–numerical solution is developed for hydrodynamic pressures on rigid dams with nonvertical upstream faces, including the effects of both compressibility and viscosity of the water. The solution is obtained by a special boundary method using a complete set of Trefftz functions, which satisfy the governing equation of motion and all boundary conditions except that at the upstream dam face. The pressure distribution is expressed as a linear combination of the natural modes of water in the reservoir and participation factors. The unknown coefficients of this expansion are obtained from the continuous treatment of the remaining boundary condition in the least-squares sense. Numerical results are presented for different geometries of the dam–liquid interface, and comparisons with other solutions are provided to show the effectiveness and efficiency of the proposed solution.
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