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

ISBN: 9783866440692 Year: Pages: VII, 190 p. DOI: 10.5445/KSP/1000005304 Language: ENGLISH
Publisher: KIT Scientific Publishing
Subject: Mathematics
Added to DOAB on : 2019-07-30 20:02:02

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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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