Commun. Comput. Phys., 9 (2011), pp. 1117-1127.

Asymptotic Analysis of Lattice Boltzmann Outflow Treatments

Michael Junk 1, Zhaoxia Yang 1*

1 FB Mathematik und Statistik, Universitat Konstanz, Postfach D194, 78457 Konstanz, Germany.

Received 9 October 2009; Accepted (in revised version) 29 September 2010
Available online 24 December 2010


We show the methodology and advantages of asymptotic analysis when applied to lattice Boltzmann outflow treatments. On the one hand, one can analyze outflow algorithms formulated directly in terms of the lattice Boltzmann variables, like the extrapolation method, to find the induced outflow conditions in terms of the Navier-Stokes variables. On the other hand, one can check the consistency and accuracy of lattice Boltzmann outflow treatments to given hydrodynamic outflow conditions like the Neumann or average pressure condition. As example how the gained insight can be used, we propose an improvement of the well known extrapolation method.

AMS subject classifications: 65N06, 76D05, 82C40

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Key words: Outflow condition, asymptotic analysis, lattice Boltzmann method.

*Corresponding author.
Email: (M. Junk), (Z. Yang)

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