The cumulant lattice Boltzmann method
Dr. Martin Geier
Institut für Rechnergestützte Modellierung im Bauingenieurwesen (iRMB)
Technische Universität Braunschweig
Abstract:
Lattice Boltzmann models using multiple relaxation times are usually based on a
moment transform using an orthogonal matrix. Despite the popularity of this approach
it has never been explained in literature why the matrix should be orthogonal. In this
talk, I will show that the orthogonality of the matrix is not only useless but harmful for
both accuracy and stability. It is shown by asymptotic analysis that orthogonalization
leads to negative transport coefficients that render the method unstable for low
viscosities. The cumulant lattice Boltzmann method is introduced as an alternative
way of decoupling the degrees of freedom with different relaxation rates. Cumulants
are directly derived from the proposition that quantities evolving with different rates
are mutually independent random variables. It is shown both analytically and
numerically that a lattice Boltzmann method based on a cumulant transform is more
accurate and stable than a lattice Boltzmann method based on a moment transform.
Literature:
The cumulant lattice Boltzmann equation in three dimensions: Theory and validation,
CMWA Vol 70. Iss. 4 pp. 507-547 (2015)

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