Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 300, Issue -, Pages 70-91Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2015.07.045
Keywords
Lattice Boltzmann method; Convection-diffusion equations; Robin boundary conditions; Curved boundaries; Asymptotic analysis
Funding
- National Natural Science Foundation of China (NSFC) [11471185]
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In this paper, we employ an asymptotic analysis technique and construct two boundary schemes accompanying the lattice Boltzmann method for convection-diffusion equations with general Robin boundary conditions. One scheme is for straight boundaries, with the boundary points locating at any distance from the lattice nodes, and has second-order accuracy. The other is for curved boundaries, has only first-order accuracy and is much simpler than the existing schemes. Unlike those in the literature, our schemes involve only the current lattice node. Such a single-node boundary schemes are highly desirable for problems with complex geometries. The two schemes are validated numerically with a number of examples. The numerical results show the utility of the constructed schemes and very well support our theoretical predications. (C) 2015 Elsevier Inc. All rights reserved.
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