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However, as the order of the scheme increases, the computational time also increases. In this work, we propose a new high-order flux reconstruction in the framework of finite volume (FV) schemes for linear problems. In particular, it is applied to solve the Linearized Euler Equations, which are widely used in the field of Computational Aeroacoustics. This new reconstruction is very efficient and well suited in the context of very high-order FV schemes, where the computation of high-order flux integrals are needed at cell edges\/faces. Different benchmark test cases are carried out to analyze the accuracy and the efficiency of the proposed flux reconstruction. The proposed methodology preserves the accuracy while the computational time relatively reduces drastically as the order increases.<\/jats:p>","DOI":"10.1007\/s00366-024-02039-2","type":"journal-article","created":{"date-parts":[[2024,8,6]],"date-time":"2024-08-06T13:08:23Z","timestamp":1722949703000},"page":"667-680","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A very fast high-order flux reconstruction for Finite Volume schemes for Computational Aeroacoustics"],"prefix":"10.1007","volume":"41","author":[{"given":"Luis","family":"Ram\u00edrez","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Javier","family":"Fern\u00e1ndez-Fidalgo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jos\u00e9","family":"Par\u00eds","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Deligant","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sofiane","family":"Khelladi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xes\u00fas","family":"Nogueira","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,8,6]]},"reference":[{"issue":"10","key":"2039_CR1","doi-asserted-by":"publisher","first-page":"1788","DOI":"10.2514\/3.12728","volume":"33","author":"CKW Tam","year":"1995","unstructured":"Tam CKW (1995) Computational acoustics: issues and methods. 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