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Numerical analysis of lattice Boltzmann methods for the heat equation on a bounded interval
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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.
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Numerical analysis of lattice Boltzmann methods for the heat equation on a bounded interval, Jan-Philipp Weiß
- Language
- Released
- 2006
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- Title
- Numerical analysis of lattice Boltzmann methods for the heat equation on a bounded interval
- Language
- German
- Authors
- Jan-Philipp Weiß
- Publisher
- Univ.-Verl. Karlsruhe
- Released
- 2006
- Format
- Paperback
- ISBN10
- 3866440693
- ISBN13
- 9783866440692
- Category
- University and college textbooks
- 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.