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

Published online by Cambridge University Press:  03 June 2015

Tobias Gebäck and
Alexei Heintz
Tobias Gebäck*
Affiliation:
Department of Mathematical Sciences, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden
Alexei Heintz*
Affiliation:
Department of Mathematical Sciences, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden
*
Corresponding author.Email:tobias.geback@chalmers.se
Email:heintz@chalmers.se
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Abstract

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.

Keywords

76R5076M2865N75Lattice Boltzmanndiffusionadvection-diffusionNeumann boundary condition

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 15 , Issue 2 , February 2014, pp. 487 - 505
Copyright
Copyright © Global Science Press Limited 2014

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