Regensburg 2019 – wissenschaftliches Programm
DY 51.2: Poster
Donnerstag, 4. April 2019, 15:00–18:00, Poster B2
Semi-automatic construction of Lattice Boltzmann models — •Dominic Spiller1 and Burkhard Duenweg1,2 — 1Max Planck Institute for Polymer Research, Mainz, Germany — 2Department of Chemical Engineering, Monash University, Melbourne, Australia
A crucial step in constructing a Lattice Boltzmann model is the definition of a suitable set of lattice velocities, and the correct assignment of the associated weights. The poster outlines the functioning of a publicly available Python script which has been written to assist researchers in that task. The speed of sound cs is considered as a parameter, which can, within limits, be chosen at will. Under this premise, the Maxwell–Boltzmann constraint equations are a system of linear equations to determine the weights, and hence amenable to numerical solution by standard linear algebra library routines. By suitable contractions, the tensor equations are mapped to a set of equivalent scalar equations, which simplifies the treatment significantly. Using a singular-value decomposition, the software is able to distinguish between (i) no solution, (ii) one unique solution, and (iii) infinitely many solutions. Case (ii) is analyzed in detail, and the range of permitted cs values is calculated. The script can treat arbitrary spatial dimensions, and an arbitrarily large degree of isotropy, measured in terms of tensorial velocity moments of the weights. New models that have been found in two and three dimensions are isotropic up to tenth order.