Coupled acoustic response of two-dimensional bounded and unbounded domains using doubly-asymptotic open boundaries

A high-order doubly-asymptotic open boundary for modelling scalar wave propagation in two-dimensional unbounded media is presented. The proposed method is capable of handling domains with arbitrary geometry by using a circular boundary to divide these into near field and far field. The original doubly-asymptotic continued-fraction approach for the far field is improved by introducing additional factor coefficients. Additionally, low-order modes are approximated by singly-asymptotic expansions only to increase the robustness of the formulation. The scaled boundary finite element method is employed to model wave propagation in the near field. Here, the frequency-dependent impedance of bounded subdomains is also expanded into a series of continued fractions. Only three to four terms per wavelength are required to obtain accurate results. The continued-fraction solutions for the bounded domain and the proposed high-order doubly-asymptotic open boundary are expressed in the time-domain as coupled ordinary differential equations, which can be solved by standard time-stepping schemes. Numerical examples are presented to demonstrate the accuracy and robustness of the proposed method, as well as its advantage over existing singly-asymptotic open boundaries.