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

• Tác giả: Jan-Philipp Weiß
• Ngôn ngữ: eng
• ISBN-13: 978-3866440692
• ISBN: KSP/1000005304
• Ký hiệu phân loại: 518.64 Numerical solutions of partial differential equations
• Thông tin xuất bản: Karlsruhe : KIT Scientific Publishing, 2006
• Mô tả vật lý: 1 electronic resource (VII, 190 p. p.)
• Bộ sưu tập: Tài liệu truy cập mở
• ID: 202798

Tóm tắt

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.