Parallel computing using Schwarz Domain Decomposition method for aeroacoustic problems

Abstract

A Domain Decomposition (DD) method for solving time-harmonic aeroacoustic problems is presented. The computational domain is decomposed into subdomains, and the aerodynamic-aeroacoustic boundary-value problem is solved independently for each subdomain. On the artificially introduced subdomain boundaries impedance-type transmission conditions are imposed, which assure the uniqueness of the solution. The Finite Element method is used to discretize the subdomain problems. A direct solver (LU factorization) is used to solve the subdomain systems of equations and an iterative scheme updates the transmission conditions to recover the global solution. This DD method is applied to solve the classical problem of a thin airfoil in a transverse gust. The problem is formulated in terms of the unsteady pressure, and exact non-reflecting conditions are imposed on the outer computational boundary. The accuracy of the numerical scheme is validated by comparison with existing solutions for both the near-field unsteady pressure and the farfiled radiated sound. The convergence as well as the computational time and memory requirements of the present method are investigated. It is shown that by combining the subdomain direct solvers with global iterations, this DD method significantly reduces both the computational time and the memory requirements. The present algorithm is particularly suited for parallel computing.