Commun. Comput. Phys., 15 (2014), pp. 487-505.

A Lattice Boltzmann Method for the Advection-Diffusion Equation with Neumann Boundary Conditions

Tobias Geback 1*, Alexei Heintz 1

1 Department of Mathematical Sciences, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden.

Received 16 November 2012; Accepted (in revised version) 23 July 2013
Available online 27 September 2013


In this paper, we study a lattice Boltzmann method for the advection-diffusion equation with Neumann boundary conditions on general boundaries. A novel mass conservative scheme is introduced for implementing such boundary conditions, and is analyzed both theoretically and numerically. Second order convergence is predicted by the theoretical analysis, and numerical investigations show that the convergence is at or close to the predicted rate. The numerical investigations include time-dependent problems and a steady-state diffusion problem for computation of effective diffusion coefficients.

AMS subject classifications: 76R50, 76M28, 65N75

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Key words: Lattice Boltzmann, diffusion, advection-diffusion, Neumann boundary condition.

*Corresponding author.
Email: (T. Geback), (A. Heintz)

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