Numerical analysis of Lattice Boltzmann Methods for the heat equation on a bounded interval

By: Material type: ArticleArticleLanguage: English Publication details: KIT Scientific Publishing 2006Description: 1 electronic resource (VII, 190 p. p.)ISBN:
  • KSP/1000005304
  • 9783866440692
Subject(s): Online resources: Summary: 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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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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