Application of H–W boundary condition in dam–reservoir interaction problem

One of the most efficient techniques for considering the unbounded media in a mathematical model is the local non-reflecting boundary conditions (NRBCs). A relatively recent approach in this context is the one proposed by Hagstrom and Warburton (H–W boundary condition). This approach is available for scalar wave equation. This equation governs the hydrodynamic pressure distribution inside a reservoir and hence, the H–W boundary condition may be used to solve the corresponding problems. A well-known case in which one has to deal with the dynamic analysis of unbounded reservoir is the dam–reservoir interaction problem. In this study the H–W NRBC has been applied to this problem and its harmonic response is calculated. By comparing the results with the exact solution, the performance and accuracy of this NRBC is examined. The numerical results confirm the very good behavior of the NRBC in the frequencies above the fundamental frequency of the reservoir. However, below this frequency range, this boundary condition does not perform very well, especially when it is applied in close distances from the dam.

► We have used the HW boundary condition for acoustic–structure interaction problem.
► We have included the effect of reservoir bottom absorption in the formulation of the boundary condition.
► The effect of evanescent modes is not included.
► Increasing the order of the boundary condition results in a fairly fast convergence in high frequencies.
► Below the cutoff frequency, some oscillatory behaviors are observed in higher orders.