{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T18:07:11Z","timestamp":1754158031832,"version":"3.41.2"},"reference-count":18,"publisher":"Emerald","issue":"8","license":[{"start":{"date-parts":[[2007,11,20]],"date-time":"2007-11-20T00:00:00Z","timestamp":1195516800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2007,11,20]]},"abstract":"<jats:sec><jats:title content-type=\"abstract-heading\">Purpose<\/jats:title><jats:p>This paper aims to focus on the temporal and spatial fourth\u2010order finite volume discretization of the incompressible form of the Navier\u2010Stokes equations on structured uniform grids. The main purpose of the paper is to assess the accuracy enhancement with the inclusion of a high\u2010order reconstruction of the point\u2010wise velocity field on a fourth\u2010order accurate numerical scheme for the solution of the unsteady incompressible Navier\u2010Stokes equations.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Design\/methodology\/approach<\/jats:title><jats:p>The present finite volume method uses a fractional time\u2010step for decoupling velocity and pressure. A Runge\u2010Kutta integration scheme is implemented for integrating the momentum equation along with a polynomial interpolation and Simpson formula for space\u2010integration. The formulation is based on step\u2010by\u2010step de\u2010averaging process applied to the velocity field.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Findings<\/jats:title><jats:p>The reconstruction of the point\u2010wise velocity field on a higher\u2010order basis is essential to obtain solutions that effectively stand for a fourth\u2010order approximation of the point\u2010wise one. Results are provided for the Taylor vortex decay problem and for co\u2010 and counter\u2010rotating vortices to assess the increase in accuracy promoted by the inclusion of the high\u2010order de\u2010averaging procedure.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Research limitations\/implications<\/jats:title><jats:p>High\u2010order reconstruction of the point\u2010wise velocity field should be considered in high\u2010order finite volume methods for the solution of the unsteady incompressible form of the Navier\u2010Stokes equations on structured grids.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Practical implications<\/jats:title><jats:p>The inclusion of a high\u2010order reconstruction of the point\u2010wise velocity field is a simple and effective method of enhancing the accuracy of a finite volume code for the computational fluid dynamics analysis.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Originality\/value<\/jats:title><jats:p>The paper develops an improved version of a fourth\u2010order accurate finite volume projection method with the inclusion of a high\u2010order reconstruction step.<\/jats:p><\/jats:sec>","DOI":"10.1108\/02644400710833279","type":"journal-article","created":{"date-parts":[[2007,10,20]],"date-time":"2007-10-20T05:28:08Z","timestamp":1192858088000},"page":"738-752","source":"Crossref","is-referenced-by-count":0,"title":["On the temporal and spatial fourth\u2010order finite volume velocity de\u2010averaging for unsteady incompressible flows simulation"],"prefix":"10.1108","volume":"24","author":[{"given":"J.M.F.","family":"Trindade","sequence":"first","affiliation":[]},{"given":"J.C.F.","family":"Pereira","sequence":"additional","affiliation":[]}],"member":"140","reference":[{"key":"key2022021520391711900_b1","doi-asserted-by":"crossref","unstructured":"Chorin, A. 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