Aeroacoustic modeling of complex flow problems: I-Domain decomposition method for the reduced wave equation

Abstract

An accurate and efficient method for solving the wave equation on multi-domains is developed for two-dimensional geometries. In this work we treat Cartesian geometries, but the method may be directly extended to more general geometries. As a first step, the one-dimensional problem is investigated. The wave equation is solved in the Fourier space. Three different numerical discretizations are tested, a Pointwise second-order accurate discretization (PT), and two fourth-order schemes: a Padè approximation (HO), and an Equation Based scheme (EB). A consistent discretization of the non reflecting boundary conditions is proposed, which preserves the overall accuracy of the corresponding interior scheme. For the solution of the linear system, it is shown that the preconditioned ILUT-GMRES method is an appropriate choice. In the multi-domain method, an optimal iterative procedure is described, specifying the correct form of the transmission conditions at the interfaces. The numerical tests confirm that the present multi-domain technique retains the same numerical properties of the single domain method. Finally the single and multi domain methods are extended to the two-dimensional case.