BENCHMARK SOLUTIONS FOR STOKES EQUATIONS WITH VARIABLE VISCOSITY IN CYLINDRICAL AND SPHERICAL COORDINATES
Stokes flows in cylindrical and spherical geometry are considered. Such flows are rather natural for geophysics. We derive some exact particular solutions of Stokes and continuity equations for particular dependence of viscosity and density on cylindrical coordinates. These solutions correspond to a...
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| Format: | Article |
| Language: | English |
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Saint Petersburg National Research University of Information Technologies, Mechanics and Optics (ITMO University)
2016-01-01
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| Series: | Naučno-tehničeskij Vestnik Informacionnyh Tehnologij, Mehaniki i Optiki |
| Subjects: | |
| Online Access: | http://ntv.ifmo.ru/file/article/14584.pdf |
| _version_ | 1818691288821661696 |
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| author | I. V. Makeev I. Y. Popov I. V. Blinova |
| author_facet | I. V. Makeev I. Y. Popov I. V. Blinova |
| author_sort | I. V. Makeev |
| collection | DOAJ |
| description | Stokes flows in cylindrical and spherical geometry are considered. Such flows are rather natural for geophysics. We derive some exact particular solutions of Stokes and continuity equations for particular dependence of viscosity and density on cylindrical coordinates. These solutions correspond to axisymmetric flows for the case when viscosity is a function of radius. We suggest exact particular solutions of Stokes and continuity equations with variable viscosity and density in spherical coordinates for the case of spherically symmetric viscosity and density distributions. We demonstrate how these solutions can be used for creation of test problems suitable for benchmarking numerical algorithms. Examples of such benchmarking are presented. The advantage of this benchmarking approach is the ability to test numerical algorithms for variable viscosity and density gradients. We suggest numerical scheme of multigrid algorithm for solving Stokes and continuity equations with variable viscosity in a spherical coordinate system. Calculations are performed on a sequence of orthogonal staggered grids. The quality of the numerical scheme was verified by comparing the numerical solution with the analytical solution of the test problem. |
| first_indexed | 2024-12-17T12:39:31Z |
| format | Article |
| id | doaj.art-4ec809cba03d46adba5e53351a3f6d33 |
| institution | Directory Open Access Journal |
| issn | 2226-1494 2500-0373 |
| language | English |
| last_indexed | 2024-12-17T12:39:31Z |
| publishDate | 2016-01-01 |
| publisher | Saint Petersburg National Research University of Information Technologies, Mechanics and Optics (ITMO University) |
| record_format | Article |
| series | Naučno-tehničeskij Vestnik Informacionnyh Tehnologij, Mehaniki i Optiki |
| spelling | doaj.art-4ec809cba03d46adba5e53351a3f6d332022-12-21T21:48:05ZengSaint Petersburg National Research University of Information Technologies, Mechanics and Optics (ITMO University)Naučno-tehničeskij Vestnik Informacionnyh Tehnologij, Mehaniki i Optiki2226-14942500-03732016-01-01161161167BENCHMARK SOLUTIONS FOR STOKES EQUATIONS WITH VARIABLE VISCOSITY IN CYLINDRICAL AND SPHERICAL COORDINATESI. V. MakeevI. Y. PopovI. V. BlinovaStokes flows in cylindrical and spherical geometry are considered. Such flows are rather natural for geophysics. We derive some exact particular solutions of Stokes and continuity equations for particular dependence of viscosity and density on cylindrical coordinates. These solutions correspond to axisymmetric flows for the case when viscosity is a function of radius. We suggest exact particular solutions of Stokes and continuity equations with variable viscosity and density in spherical coordinates for the case of spherically symmetric viscosity and density distributions. We demonstrate how these solutions can be used for creation of test problems suitable for benchmarking numerical algorithms. Examples of such benchmarking are presented. The advantage of this benchmarking approach is the ability to test numerical algorithms for variable viscosity and density gradients. We suggest numerical scheme of multigrid algorithm for solving Stokes and continuity equations with variable viscosity in a spherical coordinate system. Calculations are performed on a sequence of orthogonal staggered grids. The quality of the numerical scheme was verified by comparing the numerical solution with the analytical solution of the test problem.http://ntv.ifmo.ru/file/article/14584.pdfStokes equationsvariable viscosityGauss-Seidel methodbenchmark solutionsmultigrid methods |
| spellingShingle | I. V. Makeev I. Y. Popov I. V. Blinova BENCHMARK SOLUTIONS FOR STOKES EQUATIONS WITH VARIABLE VISCOSITY IN CYLINDRICAL AND SPHERICAL COORDINATES Naučno-tehničeskij Vestnik Informacionnyh Tehnologij, Mehaniki i Optiki Stokes equations variable viscosity Gauss-Seidel method benchmark solutions multigrid methods |
| title | BENCHMARK SOLUTIONS FOR STOKES EQUATIONS WITH VARIABLE VISCOSITY IN CYLINDRICAL AND SPHERICAL COORDINATES |
| title_full | BENCHMARK SOLUTIONS FOR STOKES EQUATIONS WITH VARIABLE VISCOSITY IN CYLINDRICAL AND SPHERICAL COORDINATES |
| title_fullStr | BENCHMARK SOLUTIONS FOR STOKES EQUATIONS WITH VARIABLE VISCOSITY IN CYLINDRICAL AND SPHERICAL COORDINATES |
| title_full_unstemmed | BENCHMARK SOLUTIONS FOR STOKES EQUATIONS WITH VARIABLE VISCOSITY IN CYLINDRICAL AND SPHERICAL COORDINATES |
| title_short | BENCHMARK SOLUTIONS FOR STOKES EQUATIONS WITH VARIABLE VISCOSITY IN CYLINDRICAL AND SPHERICAL COORDINATES |
| title_sort | benchmark solutions for stokes equations with variable viscosity in cylindrical and spherical coordinates |
| topic | Stokes equations variable viscosity Gauss-Seidel method benchmark solutions multigrid methods |
| url | http://ntv.ifmo.ru/file/article/14584.pdf |
| work_keys_str_mv | AT ivmakeev benchmarksolutionsforstokesequationswithvariableviscosityincylindricalandsphericalcoordinates AT iypopov benchmarksolutionsforstokesequationswithvariableviscosityincylindricalandsphericalcoordinates AT ivblinova benchmarksolutionsforstokesequationswithvariableviscosityincylindricalandsphericalcoordinates |