{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T17:30:25Z","timestamp":1778261425797,"version":"3.51.4"},"reference-count":25,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,11,17]],"date-time":"2023-11-17T00:00:00Z","timestamp":1700179200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science and Higher Education of the Russian Federation","award":["075-15-2022-309"],"award-info":[{"award-number":["075-15-2022-309"]}]},{"name":"Ministry of Science and Higher Education of the Russian Federation","award":["No. FSWE-2021-0009"],"award-info":[{"award-number":["No. FSWE-2021-0009"]}]},{"name":"Ministry of Science and Higher Education of the Russian Federation","award":["No. NSH-70.2022.1.5"],"award-info":[{"award-number":["No. NSH-70.2022.1.5"]}]},{"name":"Science and Universities National Project under the Young Scientists Lab Program of the RF Ministry of Education and Science","award":["075-15-2022-309"],"award-info":[{"award-number":["075-15-2022-309"]}]},{"name":"Science and Universities National Project under the Young Scientists Lab Program of the RF Ministry of Education and Science","award":["No. FSWE-2021-0009"],"award-info":[{"award-number":["No. FSWE-2021-0009"]}]},{"name":"Science and Universities National Project under the Young Scientists Lab Program of the RF Ministry of Education and Science","award":["No. NSH-70.2022.1.5"],"award-info":[{"award-number":["No. NSH-70.2022.1.5"]}]},{"name":"Council of the Grants of the President of the Russian Federation for state support of Leading Scientific Schools of the Russian Federation","award":["075-15-2022-309"],"award-info":[{"award-number":["075-15-2022-309"]}]},{"name":"Council of the Grants of the President of the Russian Federation for state support of Leading Scientific Schools of the Russian Federation","award":["No. FSWE-2021-0009"],"award-info":[{"award-number":["No. FSWE-2021-0009"]}]},{"name":"Council of the Grants of the President of the Russian Federation for state support of Leading Scientific Schools of the Russian Federation","award":["No. NSH-70.2022.1.5"],"award-info":[{"award-number":["No. NSH-70.2022.1.5"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper uses a finite volume algorithm to address the numerical modeling of fluid flow around moving bodies. The Navier\u2013Stokes equations, which describe the flow of viscous compressible gas, along with key boundary conditions and discretization schemes, are presented. As the motion of boundaries typically leads to changes in the control volumes, the basic discretization schemes need to be adapted. This paper provides a detailed discussion on the adaptation of the initial system to deforming boundaries while preserving communication topology. The method for calculating the boundary velocity is a crucial element of the numerical scheme. The paper proposes an approach to reconstruct the boundary velocity vector using deformation analysis and the condition of geometric conservation. This approach ensures correct simulation results for arbitrary unstructured computational grids. A comparison of two approaches to reconstructing the boundary velocity vector for characteristic aviation problems in the direct formulation is presented. It is shown that the proposed approach allows for more accurate modeling of object motion on arbitrary grids using the \u201cinvariant\u201d principle of the computational domain topology.<\/jats:p>","DOI":"10.3390\/sym15112081","type":"journal-article","created":{"date-parts":[[2023,11,17]],"date-time":"2023-11-17T15:30:53Z","timestamp":1700235053000},"page":"2081","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Modeling Object Motion on Arbitrary Unstructured Grids Using an Invariant Principle of Computational Domain Topology: Key Features"],"prefix":"10.3390","volume":"15","author":[{"given":"Aleksey","family":"Sarazov","sequence":"first","affiliation":[{"name":"Russian Federal Nuclear Center, All-Russian Research Institute of Experimental Physics, Nizhny Novgorod Region, Sarov 607188, Russia"},{"name":"Department of Applied Mathematics, Nizhny Novgorod State Technical University n.a. R.E. Alekseev, 24 ul. Minina, Nizhny Novgorod 603155, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3247-0835","authenticated-orcid":false,"given":"Andrey","family":"Kozelkov","sequence":"additional","affiliation":[{"name":"Russian Federal Nuclear Center, All-Russian Research Institute of Experimental Physics, Nizhny Novgorod Region, Sarov 607188, Russia"},{"name":"Department of Applied Mathematics, Nizhny Novgorod State Technical University n.a. R.E. Alekseev, 24 ul. Minina, Nizhny Novgorod 603155, Russia"},{"name":"Aircraft Design and Certification Department, Moscow Aviation Institute, Volokolamskoe Shosse, 4, Moscow 125993, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4554-0513","authenticated-orcid":false,"given":"Dmitriy","family":"Strelets","sequence":"additional","affiliation":[{"name":"Aircraft Design and Certification Department, Moscow Aviation Institute, Volokolamskoe Shosse, 4, Moscow 125993, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Roman","family":"Zhuchkov","sequence":"additional","affiliation":[{"name":"Russian Federal Nuclear Center, All-Russian Research Institute of Experimental Physics, Nizhny Novgorod Region, Sarov 607188, Russia"},{"name":"Department of Applied Mathematics, Nizhny Novgorod State Technical University n.a. R.E. Alekseev, 24 ul. Minina, Nizhny Novgorod 603155, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,17]]},"reference":[{"key":"ref_1","unstructured":"Volkov, K.N., and Emelyanov, V.N. (2003). Flow and Heat Transfer in Channels and Rotating Cavities, Publishing House of Physical and Mathematical Literature."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Meakin, R.L., and Suhs, N.E. (1989, January 13\u201315). Unsteady aerodynamic simulation of multiple bodies in relative motion. Proceedings of the 9th Computational Fluid Dynamics Conference, Buffalo, NY, USA.","DOI":"10.2514\/6.1989-1996"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/s10494-020-00180-8","article-title":"Influence of Rotating Wheels and Moving Ground Use on the Unsteady Wake of a Small-Scale Road Vehicle","volume":"106","author":"Rejniak","year":"2021","journal-title":"Flow Turbul. 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