Helmholtz’s decomposition for compressible flows and its application to computational aeroacoustics – ScienceOpen
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      Helmholtz’s decomposition for compressible flows and its application to computational aeroacoustics

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          Abstract

          The Helmholtz decomposition, a fundamental theorem in vector analysis, separates a given vector field into an irrotational (longitudinal, compressible) and a solenoidal (transverse, vortical) part. The main challenge of this decomposition is the restricted and finite flow domain without vanishing flow velocity at the boundaries. To achieve a unique and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}

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          -orthogonal decomposition, we enforce the correct boundary conditions and provide its physical interpretation. Based on this formulation for bounded domains, the flow velocity is decomposed. Combining the results with Goldstein’s aeroacoustic theory, we model the non-radiating base flow by the transverse part. Thereby, this approach allows a precise physical definition of the acoustic source terms for computational aeroacoustics via the non-radiating base flow. In a final simulation example, Helmholtz’s decomposition of compressible flow data using the finite element method is applied to an overflowed rectangular cavity at Mach 0.8. The results show a reasonable agreement with the source data and illustrate the distinct parts of the Helmholtz decomposition.

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          Most cited references29

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                Author and article information

                Contributors
                stefan.schoder@tuwien.ac.at
                Journal
                SN Partial Differ Equ Appl
                SN Partial Differ Equ Appl
                Sn Partial Differential Equations and Applications
                Springer International Publishing (Cham )
                2662-2963
                2662-2971
                6 November 2020
                6 November 2020
                2020
                : 1
                : 6
                : 46
                Affiliations
                [1 ]GRID grid.410413.3, ISNI 0000 0001 2294 748X, TU Graz, Institute of Fundamentals and Theory in Electrical Engineering, ; Inffeldgasse 18, 8010 Graz, Austria
                [2 ]GRID grid.5329.d, ISNI 0000 0001 2348 4034, TU Wien, Institute of Mechanics and Mechatronics, ; Getreidemarkt 9, 1060 Wien, Vienna Austria
                Author information
                http://orcid.org/0000-0002-2148-6703
                Article
                44
                10.1007/s42985-020-00044-w
                7648005
                dd3522df-480d-495b-9b01-6fab3ade2d89
                © The Author(s) 2020

                Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

                History
                : 12 March 2020
                : 5 October 2020
                Funding
                Funded by: FundRef http://dx.doi.org/10.13039/501100002428, Austrian Science Fund;
                Award ID: 3702
                Award Recipient :
                Funded by: FundRef http://dx.doi.org/10.13039/501100001659, Deutsche Forschungsgemeinschaft;
                Award ID: 391215328
                Funded by: Austrian Science Fund (FWF)
                Categories
                Original Paper
                Custom metadata
                © Springer Nature Switzerland AG 2020

                helmholtz’s decomposition,compressible flows,aeroacoustic,fem,76-10,68-04

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