Direct Noise Computations Using Overset Grids

Abstract

The use of overset grids allows to describe naturally the solution of a set of partial differential equations for complex computational domain when structured grids are employed. It consists in the decomposition of the domain into smaller ones and in ensuring the communications between these sub-domains by interpolations. For aeroacoustic problems, these interpolations have to be accurate enough to take into account the great disparity of scales. In this paper, Lagrange interpolations and optimized interpolations are used. We investigate which one of these two interpolation methods is the more appropriate for overset grids in aeroacoustic applie and also on the degree of accuracy needed not to degrade the solution of a problem. A Fourier analysis shows that the optimized interpolations are better than the Lagrange interpolations in the higher wavenumbers. However, there is a loss of accuracy of the optimized method in the lower wavenumbers. That is why order constraints are added to the optimization. Then, the following numerical test-cases are performed : the advection of a vortex, the propagation of a source on a Cartesian-Cartesian overlapping or a polar-Cartesian overlapping. We conclue that the optimized interpolations with the order constraints present best results on a large range of wavenumbers. Morever, the test-cases show that the accuracy and the spectral limit of the interpolations can be less than the limit of resolvability of the discretization schemes. Finally, a more complex validation case is performed with the diffraction of an harmonic source by two cylinders. A set of three grids is used and the solution presents a good behavior.