Non-reflecting boundary conditions and domain decomposition methods for industrial flow acoustics

This PhD project is devoted to non-overlapping Schwarz domain decomposition methods for the resolution of high frequency flow acoustics problems of industrial relevance. Time-harmonic solvers are difficult to parallelize due to their high-oscillatory behaviour, and current solvers quickly reach an upper frequency limit dictated by the available computer memory. Non-overlapping Schwarz methods split the domain into subdomains at the continuous level and provide a suitable setting for distributed memory parallelization. The problem is solved iteratively on the interface unknowns, where the keystone for quick convergence relies on appropriate transmission conditions. The first part of this thesis is devoted to the design of transmission operators tailored to convected and heterogeneous time-harmonic wave propagation. To this end we study two non-reflecting boundary techniques that provide local approximations to the Dirichlet-to-Neumann operator. On the one hand, Absorbing Boundary Conditions are designed based on microlocal analysis and pseudodifferential calculus. On the other hand, the convected acoustic stability issue is addressed for Perfectly Matched Layers in convex domains with Lorentz transformation. The second part of this thesis describes how to adapt a generic domain decomposition framework to flow acoustics, and applies the newly designed transmission conditions to simple academic problems. We explain the relation between the non-overlapping Schwarz formulation and an algebraic block LU factorization of the problem. Finally we propose a parallel implementation of the method and show the benefit of the approach for the three-dimensional noise radiation of a high by-pass ratio turbofan engine intake.