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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.
Nákup knihy
Numerical analysis of lattice Boltzmann methods for the heat equation on a bounded interval, Jan-Philipp Weiß
- Jazyk
- Rok vydania
- 2006
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- Titul
- Numerical analysis of lattice Boltzmann methods for the heat equation on a bounded interval
- Jazyk
- nemecky
- Autori
- Jan-Philipp Weiß
- Vydavateľ
- Univ.-Verl. Karlsruhe
- Vydavateľ
- 2006
- Väzba
- mäkká
- ISBN10
- 3866440693
- ISBN13
- 9783866440692
- Kategórie
- Skriptá a vysokoškolské učebnice
- Anotácia
- 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.