Development of optimized interpolation schemes with spurious modes minimization

Abstract

SUMMARYThis work constitutes a fraction of a more extensive effort, which ultimate objective is the development of advanced aeroacoustics hybrid methods. Within this framework, we here focus on the interpolation step, on which generally rely all coupling processes that link altogether the various stages constituting any given hybrid method. In that regard, previous works by the present authors had revealed the intrinsic limitations and subsequent side effects (e.g., signal degradation) that weight on usual high-order interpolation schemes, whether the latter are of centered or noncentered nature, as well as optimized in an acoustic sense or not. Based on the outcomes of such study, here, a novel optimization technique for interpolation schemes is proposed. Such a technique, which is designed hereafter as the interpolation by parts (IBP), allows interpolating accurately a given signal, while minimizing its possible degradation. As a result, compared with its standard counterpart, any IBP -optimized interpolation scheme exhibits improved characteristics, such as a spurious modes generation that is greatly reduced (up to a 99% factor). Such improved characteristics are here validated on the basis of three test cases (of 1D, 2D and 3D nature), which illustrates the potentialities offered by the IBP optimization technique.

An advanced hybrid method for the acoustic prediction

“…aerodynamic noise). On the same way, all the related outcomes were extensively documented through previous publications, either as journal articles or proceedings of international conferences [22][23][24][25][26][27][28][29][30][31]. The reason for summarizing these various works and associated outcomes here was that, although focusing each on a particular aspect (and deserving each an entire publication in itself), they all targeted the same common objective, which is the development of the advanced CAA-based hybrid approach that the present article is about.…”

“…In addition to deliver fundamental insights that may help optimizing any kind of acoustic hybrid method (e.g. IM-or CAA-based one), these actions led to the development of several methodological innovations (SPC criterion [25], IBP interpolator [26], IOFD schemes [29] -see below), which made it possible to relax some of the constraints preventing the present CAA-based hybrid approach to be applied to challenging problems (such as the one presented in Section 6.2). Here again, all these outcomes were thoroughly validated and/or applied through various test cases of increasing complexity, among which the ones provided in Sections 5 and 6.…”

“…non linear formulation [17,18], LOC Non Reflecting Boundary Condition [17,18,21]), several research actions were conducted [25][26][27][28][29][30], being primarily achieved by the present second author in the framework of his PhD thesis [30]. These works consisted in (i) characterizing [25,27,28] and (ii) possibly minimizing [26,29] the various impacts that its data manipulation may have onto a given acoustic signal, when the latter is to be transferred from one to another stage of an acoustic hybrid method. In addition to deliver fundamental insights that may help optimizing any kind of acoustic hybrid method (e.g.…”

“…the anechoicity requirement evocated above). Then, follow-on research actions [25][26][27][28][29][30] consisted in optimizing such overall hybrid method, for it can cope with all stringent constraints that are dictated by real-life applications without being jeopardized by some of their unavoidable side effects (e.g. signal degradation -see detail below).…”

“…those involving complex acoustic signal and/or requiring heavy computations). More precisely, works consisted in optimizing the overall hybrid procedure [25][26][27][28][29][30], for the latter can (i) cope with all stringent constraints that are dictated by real-life applications (ii) without being jeopardized by some of their unavoidable side effects (such as the signal degradation to which unsteady CFD data are subjected, when manipulated for being acoustically exploited [25]). To this end, and besides specific optimizations of the underlying CAA approach by the present first author (e.g.…”