Dispersion error control for underwater acoustic scattering problems using a coupled cell-based smoothed radial point interpolation method

Abstract

A coupled cell-based smoothed radial point interpolation method is presented by combining the cell-based smoothed radial point interpolation method (CSRPIM) and the modified Dirichlet to Neumann boundary condition (MDtN-BC) to effectively control the dispersion error in predicting acoustic scattering. In the coupled CSRPIM, the MDtN-BC is used to satisfy the Sommerfeld radiation condition approaching infinity, and a cell-based smoothing operation together with the radial point interpolation method (RPIM) is adopted to soften the acoustic stiffness of the numerical model. The condensed RPIM shape functions are created by using real and virtual nodes, and virtual node selection schemes are studied to appropriately soften the stiffness. A major advantage of the coupled CSRPIM is that it can achieve very close-to-exact stiffness of the original model without introducing extra degrees of freedom. The properties of the proposed method are numerically studied. Simulations indicate that the six-virtual-node selection scheme performs the best. The results reveal that the developed method can significantly reduce the dispersion error and has excellent computational performance. In addition, the developed method shows good potential for practical acoustic-scattering prediction in engineering applications.