Performance of under-resolved two-dimensional incompressible flow simulations, II
Journal of Computational Physics
A novel thermal model for the lattice Boltzmann method in incompressible limit
Journal of Computational Physics
Implementation aspects of 3D lattice-BGK: boundaries, accuracy, and a new fast relaxation method
Journal of Computational Physics
Lattice Boltzmann method for 3-D flows with curved boundary
Journal of Computational Physics
SIAM Journal on Scientific Computing
Numerical Simulation of the Taylor-Green Vortex
Proceedings of the International Symposium on Computing Methods in Applied Sciences and Engineering, Part 2
Incompressible limits of lattice Boltzmann equations using multiple relaxation times
Journal of Computational Physics
Mathematics and Computers in Simulation - Special issue: Discrete simulation of fluid dynamics in complex systems
Journal of Computational Physics
Journal of Computational Physics
An interpretation and derivation of the lattice Boltzmann method using Strang splitting
Computers & Mathematics with Applications
Turbulent jet computations based on MRT and Cascaded Lattice Boltzmann models
Computers & Mathematics with Applications
Hi-index | 31.45 |
The vast majority of lattice Boltzmann algorithms produce a non-Galilean invariant viscous stress. This defect arises from the absence of a term in the third moment, the equilibrium heat flow tensor, proportional to the cube of the fluid velocity. This moment cannot be specified independently of the lower moments on the standard lattices such as D2Q9, D3Q15, D3Q19 or D3Q27. A partial correction has recently been demonstrated that restores some of these missing cubic terms on the D2Q9 and D3Q27 tensor product lattices. This correction restores Galilean invariance for shear flows aligned with the coordinate axes, but flows inclined at arbitrary angles may show larger errors than before. These remaining errors are due to the diagonal terms of the equilibrium heat flow tensor, which cannot be corrected on standard lattices. However, the remaining errors may be largely absorbed by introducing a matrix collision operator with velocity-dependent collision rates for the diagonal components of the momentum flux tensor. This completely restores Galilean invariance for flows with uniform density, and in general reduces the magnitude of the defect in Galilean invariance from Mach number cubed to Mach number to the fifth power. The effectiveness of the resulting algorithm is demonstrated by comparisons with the standard and partially corrected lattice Boltzmann algorithms for two- and three-dimensional flows.