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High-order regularization in lattice-Boltzmann equations

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Mattila, K., Philippi, P. C., & Hegele, L. A., Jr. (2017). High-order regularization in lattice-Boltzmann equations. Physics of Fluids, 29 (4), 046103. doi:10.1063/1.4981227
Published in
Physics of Fluids
Authors
Mattila, Keijo |
Philippi, Paulo C. |
Hegele, Luiz A.
Date
2017
Copyright
© AIP Publishing, 2017. This is a final draft version of an article whose final and definitive form has been published by AIP. Published in this repository with the kind permission of the publisher.

 
A lattice-Boltzmann equation (LBE) is the discrete counterpart of a continuous kinetic model. It can be derived using a Hermite polynomial expansion for the velocity distribution function. Since LBEs are characterized by discrete, finite representations of the microscopic velocity space, the expansion must be truncated and the appropriate order of truncation depends on the hydrodynamic problem under investigation. Here we consider a particular truncation where the non-equilibrium distribution is expanded on a par with the equilibrium distribution, except that the diffusive parts of high-order nonequilibrium moments are filtered, i.e., only the corresponding advective parts are retained after a given rank. The decomposition of moments into diffusive and advective parts is based directly on analytical relations between Hermite polynomial tensors. The resulting, refined regularization procedure leads to recurrence relations where high-order non-equilibrium moments are expressed in terms of low-order ones. The procedure is appealing in the sense that stability can be enhanced without local variation of transport parameters, like viscosity, or without tuning the simulation parameters based on embedded optimization steps. The improved stability properties are here demonstrated using the perturbed double periodic shear layer flow and the Sod shock tube problem as benchmark cases. ...
Publisher
American Institute of Physics
ISSN Search the Publication Forum
1070-6631
Keywords
polynomials subspaces tensor methods: shock tubes recurrence relations
DOI
10.1063/1.4981227
URI

http://urn.fi/URN:NBN:fi:jyu-201704272101

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