Domain-Decomposition Method for Time-Harmonic Aeroacoustic Problems

Abstract

A domain-decomposition (DD) method is developed for parallel computation of time-harmonic aerodynamic ‐ aeroacoustic problems. The computational domain is decomposed into subdomains, and the aerodynamic ‐ aeroacoustic boundary-value problem is solved independently for each subdomain. Impedance-type transmission conditions are imposed on the artie cially introduced subdomain boundaries to ensure the uniqueness of the solution. A Dirichlet-to-Neumann map is used as a nonree ecting radiation condition along the outer computational boundary. Subdomain problems are then solved using the e nite element method, and an iterative scheme updates the transmission conditions to recover the global solution. The present algorithm is implemented for two model problems. First, the sound radiated from a surface simulating a two-dimensional monopole is calculated using an unstructured mesh. Second, the e ow about a thin airfoil in a transverse gust is computed using a structured mesh. The accuracy of the numerical scheme is validated by comparison with existing solutions for both the near-e eld unsteady pressure and the far-e eld radiated sound. The convergence and the computational time and memory requirements of the present method are studied. It is shown that by combining the subdomain direct solvers with global iterations this DD method signie cantly reduces both the computational time and memory requirements.