Numerical analysis of Lattice Boltzmann Methods for the heat equation on a bounded interval
Lattice Boltzmann methods are a promising approach for the numerical solution of fluid-dynamic problems. We consider the one-dimensional Goldstein-Taylor model with the aim to answer some of the questions concerning the numerical analysis of lattice Boltzmann schemes. Discretizations for the solutio...
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| Formato: | Online |
| Idioma: | inglês |
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KIT Scientific Publishing
2021
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| Acesso em linha: | 35592 |
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| _version_ | 1869530633374531584 |
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| author | Weiß, Jan-Philipp |
| author_browse | Weiß, Jan-Philipp |
| author_facet | Weiß, Jan-Philipp |
| author_sort | Weiß, Jan-Philipp |
| collection | Directory of Open Access Books |
| description | Lattice Boltzmann methods are a promising approach for the numerical solution of fluid-dynamic problems. We consider the one-dimensional Goldstein-Taylor model with the aim to answer some of the questions concerning the numerical analysis of lattice Boltzmann schemes. Discretizations for the solution of the heat equation are presented for a selection of boundary conditions. Stability and convergence of the solutions are proved by employing energy estimates and explicit Fourier representations. |
| format | Online |
| id | doab-20.500.12854ir-54912 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | KIT Scientific Publishing |
| publisherStr | KIT Scientific Publishing |
| record_format | ojs |
| spelling | doab-20.500.12854ir-549122023-12-20T18:40:38Z Numerical analysis of Lattice Boltzmann Methods for the heat equation on a bounded interval Weiß, Jan-Philipp QA1-939 CFD Konvergenz Lattice-Boltzmann Numerische Strömungssimulation Gitter-Boltzmann-Methode Wärmeleitungsgleichung Heat Equation Convergence bic Book Industry Communication::P Mathematics & science Lattice Boltzmann methods are a promising approach for the numerical solution of fluid-dynamic problems. We consider the one-dimensional Goldstein-Taylor model with the aim to answer some of the questions concerning the numerical analysis of lattice Boltzmann schemes. Discretizations for the solution of the heat equation are presented for a selection of boundary conditions. Stability and convergence of the solutions are proved by employing energy estimates and explicit Fourier representations. 2021-02-11T21:19:33Z 2021-02-11T21:19:33Z 2019-07-30 20:02:02 2006 book 35592 9783866440692 https://directory.doabooks.org/handle/20.500.12854/54912 eng image/jpeg https://www.ksp.kit.edu/9783866440692 KIT Scientific Publishing 10.5445/KSP/1000005304 10.5445/KSP/1000005304 68fffc18-8f7b-44fa-ac7e-0b7d7d979bd2 9783866440692 VII, 190 p. open access |
| spellingShingle | QA1-939 CFD Konvergenz Lattice-Boltzmann Numerische Strömungssimulation Gitter-Boltzmann-Methode Wärmeleitungsgleichung Heat Equation Convergence bic Book Industry Communication::P Mathematics & science Weiß, Jan-Philipp Numerical analysis of Lattice Boltzmann Methods for the heat equation on a bounded interval |
| title | Numerical analysis of Lattice Boltzmann Methods for the heat equation on a bounded interval |
| title_full | Numerical analysis of Lattice Boltzmann Methods for the heat equation on a bounded interval |
| title_fullStr | Numerical analysis of Lattice Boltzmann Methods for the heat equation on a bounded interval |
| title_full_unstemmed | Numerical analysis of Lattice Boltzmann Methods for the heat equation on a bounded interval |
| title_short | Numerical analysis of Lattice Boltzmann Methods for the heat equation on a bounded interval |
| title_sort | numerical analysis of lattice boltzmann methods for the heat equation on a bounded interval |
| topic | QA1-939 CFD Konvergenz Lattice-Boltzmann Numerische Strömungssimulation Gitter-Boltzmann-Methode Wärmeleitungsgleichung Heat Equation Convergence bic Book Industry Communication::P Mathematics & science |
| topic_facet | QA1-939 CFD Konvergenz Lattice-Boltzmann Numerische Strömungssimulation Gitter-Boltzmann-Methode Wärmeleitungsgleichung Heat Equation Convergence bic Book Industry Communication::P Mathematics & science |
| url | 35592 |
| work_keys_str_mv | AT weißjanphilipp numericalanalysisoflatticeboltzmannmethodsfortheheatequationonaboundedinterval |