A sharp-interface Cartesian grid method for time-domain acoustic scattering from complex geometries

Abstract

This paper is concerned with the development of a Cartesian grid method for predicting the acoustic field scattered by complex geometries immersed in an infinite fluid. The sound wave in the fluid is formulated by the linearized Euler equations (LEEs), which are computed on a fixed Cartesian grid by using a fourth-order dispersion-relation-preserving (DRP) scheme. The solid object naturally cuts the underlying Cartesian grid with its geometrical boundary, which is modeled by the Lagrangian method. A sharp-interface Cartesian grid model based on the ghost-cell immersed boundary method is established to impose the non-penetrating conditions on the complex boundary of the solid. The values of the acoustic variables at the ghost points are constructed by a linear extrapolation in conjunction with a constrained moving least-squares (CMLS) interpolation method. The interpolation method is capable of eliminating the numerical instability encountered in the conventional moving least-squares (MLS) formulation. The perfectly matched layers are adopted to absorb the out-going sound waves without any reflections from the computational boundary to the interior domain. The proposed method is verified by several benchmark problems in computational aeroacoustics, including the initial value problem of a pressure perturbation scattered by a rigid cylinder, and Gaussian distributed acoustic sources scattered by a single cylinder or two cylinders. Application of the proposed method to the problem of acoustic waves scattered by solids with complex geometries is also presented to demonstrate the effectiveness and robustness of the method.