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Numerical Analysis of Lattice Boltzmann Methods for the Heat Equation on a Bounded Interval

Posted By: step778
Numerical Analysis of Lattice Boltzmann Methods for the Heat Equation on a Bounded Interval

Jan-Philipp Weiß, "Numerical Analysis of Lattice Boltzmann Methods for the Heat Equation on a Bounded Interval"
2006 | pages: 208 | ISBN: 3866440693 | PDF | 9,6 mb

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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