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Updated: Nov 5, 2025

Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence
Published on: June 24, 2016
Rotational symmetry of the multiple-relaxation-time collision model
1Department of Mechanics and Aerospace Engineering, Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Shenzhen Key Laboratory of Complex Aerospace Flows, Southern University of Science and Technology, Shenzhen 518055, China.
Abstract:
We point out that the minimal components of the tensorial moments of the distribution that can be independently relaxed in collision without violating rotational symmetry are its irreducible representation (irrep) of SO(3), and a generic multiple-relaxation-time collision model can be constructed by independently relaxing these components. As the simplest example the irreps of the second moment are the traceless deviatoric stress and an isotropic tensor which is conserved in monatomic gases. Applying the decomposition to the thermal lattice Boltzmann model for polyatomic gases [Phys. Rev. E 77, 035701(R) (2008)PRESCM1539-375510.1103/PhysRevE.77.035701], the shear and bulk viscosities are decoupled by two independent relaxation times. The hydrodynamic equation of the model is obtained via Chapman-Enskog calculation and verified by numerical simulation.
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