{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:38:35Z","timestamp":1760240315795,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2019,5,9]],"date-time":"2019-05-09T00:00:00Z","timestamp":1557360000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51609056"],"award-info":[{"award-number":["51609056"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In order to numerically investigate the free surface flow evolution in a cylindrical tank, a regular structured grid system in the cylindrical coordinates is usually applied to solve control equations based on the incompressible two-phase flow model. Since the grid spacing in the azimuthal direction is proportionate to the radial distance in a regular structured grid system, very small grid spacing would be obtained in the azimuthal direction and it would require a very small computational time step to satisfy the stability restriction. Moreover, serious mass disequilibrium problems may happen through the convection of the free surface with the Volume of Fluid (VOF) method. Therefore in the present paper, the zonal embedded grid technique was implemented to overcome those problems by gradually adjusting the mesh resolution in different grid blocks. Over the embedded grid system, a finite volume algorithm was developed to solve the Navier\u2013Stokes equations in the three-dimensional cylindrical coordinates. A high-resolution scheme was applied to resolve the free surface between the air and water phases based on the VOF method. Computation of liquid convection under a given velocity field shows that the VOF method implemented with a zonal embedded grid is more advanced in keeping mass continuity than that with regular structured grid system. Furthermore, the proposed model was also applied to simulate the sharp transient evolution of circular dam breaking flow. The simulation results were validated against the commercial software Fluent, which shows a good agreement, and the proposed model does not yield any free surface oscillation.<\/jats:p>","DOI":"10.3390\/a12050098","type":"journal-article","created":{"date-parts":[[2019,5,9]],"date-time":"2019-05-09T11:22:35Z","timestamp":1557400955000},"page":"98","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Free Surface Flow Simulation by a Viscous Numerical Cylindrical Tank"],"prefix":"10.3390","volume":"12","author":[{"given":"Xingyue","family":"Ren","sequence":"first","affiliation":[{"name":"College of Civil Engineering and Architecture, Hainan University, Haikou 570228, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fangjie","family":"Xiong","sequence":"additional","affiliation":[{"name":"College of Civil Engineering and Architecture, Hainan University, Haikou 570228, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ke","family":"Qu","sequence":"additional","affiliation":[{"name":"School of Hydraulic Engineering, Changsha University of Science &amp; Technology, Changsha 410114, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Norimi","family":"Mizutani","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, Nagoya University, Nagoya 464-8602, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3364","DOI":"10.1016\/j.engstruct.2007.08.023","article-title":"Nonlinear sloshing response of cylindrical tanks subjected to earthquake ground motion","volume":"29","year":"2007","journal-title":"Eng. 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