Analysis of acoustic radiation problems using the cell-based smoothed radial point interpolation method with Dirichlet-to-Neumann boundary condition

Abstract

In this work, the cell-based smoothed radial point interpolation method (CSRPIM) with Dirichlet-to-Neumann (DtN) boundary condition is presented to resolve acoustic radiation problems. In the scheme of CSRPIM, additional virtual nodes are used in RPIM shape functions creation, which, together with the operation of cell-based gradient smoothing operation, enable the model provide proper stiffness for acoustic field without extra degrees of freedom. It is demonstrated that the present CSRPIM can reduce the dispersion error significantly and possess some superiorities, such as high accuracy and insensitivity to mesh distortion. For exterior acoustic problems, the well-known DtN artificial boundary has been employed to ensure that there are no spurious reflections from unbounded domain. Several numerical examples have been studied to verify the properties of the present CSRPIM with DtN condition. The results show that this CSRPIM is outstanding to tackle acoustic radiation problems and can generate more reasonable solutions than the standard FEM. Also, owing to the use of linear background mesh, the present method has a good potential to be applied to practical acoustic radiation engineering problems.