{"title":"求解高频振动对流问题的有效多重网格法","authors":"A. I. Fedyushkin, K. A. Ivanov, A. A. Puntus","doi":"10.1134/S1990478923020096","DOIUrl":null,"url":null,"abstract":"<p> The paper describes an implemented algorithm for solving the problem of vibrational\nconvection in a rectangular domain filled with an unevenly heated incompressible fluid. The\nmathematical model is based on the solution of the Simonenko–Zenkovskaya equations obtained\nby averaging the Navier-Stokes equations under the assumption that the volume of liquid executes\nhigh-frequency translational vibrations. To solve the Poisson equations, an algebraic multigrid\nmethod is implemented in combination with a highly efficient dynamic programming method\n(based on R. Bellman’s optimal control principle) and fast Fourier transform. Mathematical\nsoftware written in <span>C/C++</span> has\nbeen developed. Examples of solving model problems with various directions of the heating flow of\na square domain relative to the vibration vector are given.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 2","pages":"307 - 319"},"PeriodicalIF":0.5800,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An Effective Multigrid Method for Solving Problems of High-Frequency Vibrational Convection\",\"authors\":\"A. I. Fedyushkin, K. A. Ivanov, A. A. Puntus\",\"doi\":\"10.1134/S1990478923020096\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p> The paper describes an implemented algorithm for solving the problem of vibrational\\nconvection in a rectangular domain filled with an unevenly heated incompressible fluid. The\\nmathematical model is based on the solution of the Simonenko–Zenkovskaya equations obtained\\nby averaging the Navier-Stokes equations under the assumption that the volume of liquid executes\\nhigh-frequency translational vibrations. To solve the Poisson equations, an algebraic multigrid\\nmethod is implemented in combination with a highly efficient dynamic programming method\\n(based on R. Bellman’s optimal control principle) and fast Fourier transform. Mathematical\\nsoftware written in <span>C/C++</span> has\\nbeen developed. Examples of solving model problems with various directions of the heating flow of\\na square domain relative to the vibration vector are given.\\n</p>\",\"PeriodicalId\":607,\"journal\":{\"name\":\"Journal of Applied and Industrial Mathematics\",\"volume\":\"17 2\",\"pages\":\"307 - 319\"},\"PeriodicalIF\":0.5800,\"publicationDate\":\"2023-08-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied and Industrial Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1990478923020096\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Engineering\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478923020096","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
An Effective Multigrid Method for Solving Problems of High-Frequency Vibrational Convection
The paper describes an implemented algorithm for solving the problem of vibrational
convection in a rectangular domain filled with an unevenly heated incompressible fluid. The
mathematical model is based on the solution of the Simonenko–Zenkovskaya equations obtained
by averaging the Navier-Stokes equations under the assumption that the volume of liquid executes
high-frequency translational vibrations. To solve the Poisson equations, an algebraic multigrid
method is implemented in combination with a highly efficient dynamic programming method
(based on R. Bellman’s optimal control principle) and fast Fourier transform. Mathematical
software written in C/C++ has
been developed. Examples of solving model problems with various directions of the heating flow of
a square domain relative to the vibration vector are given.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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