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Volume 15, Issue 2
A Lattice Boltzmann Method for the Advection-Diffusion Equation with Neumann Boundary Conditions

Tobias Gebäck & Alexei Heintz

DOI: 10.4208/cicp.161112.230713a

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

Published online: 2014-02

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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.

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@Article{CiCP-15-487, author = {Tobias Gebäck and Alexei Heintz}, title = {A Lattice Boltzmann Method for the Advection-Diffusion Equation with Neumann Boundary Conditions}, journal = {Communications in Computational Physics}, year = {2014}, volume = {15}, number = {2}, pages = {487--505}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.161112.230713a}, url = {http://global-sci.org/intro/article_detail/cicp/7103.html} }
TY - JOUR T1 - A Lattice Boltzmann Method for the Advection-Diffusion Equation with Neumann Boundary Conditions AU - Tobias Gebäck & Alexei Heintz JO - Communications in Computational Physics VL - 2 SP - 487 EP - 505 PY - 2014 DA - 2014/02 SN - 15 DO - http://doi.org/10.4208/cicp.161112.230713a UR - https://global-sci.org/intro/article_detail/cicp/7103.html KW - AB -

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.

Tobias Gebäck and Alexei Heintz. (2014). A Lattice Boltzmann Method for the Advection-Diffusion Equation with Neumann Boundary Conditions. Communications in Computational Physics. 15 (2). 487-505. doi:10.4208/cicp.161112.230713a
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