Numerical analysis of Lattice Boltzmann Methods for the heat equation on a bounded interval
Abstract
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.
Keywords
CFD; Konvergenz; Lattice-Boltzmann; Numerische Strömungssimulation; Gitter-Boltzmann-Methode; Wärmeleitungsgleichung; Heat Equation; ConvergenceISBN
9783866440692Publisher
KIT Scientific PublishingPublisher website
http://www.ksp.kit.edu/Publication date and place
2006Classification
Mathematics & science