A general analysis of the hydrodynamic limit of multi-relaxation time lattice Boltzmann models is presented.We examine multi-relaxation time BGK collision operators that are constructed similarly to those for the MRT ...A general analysis of the hydrodynamic limit of multi-relaxation time lattice Boltzmann models is presented.We examine multi-relaxation time BGK collision operators that are constructed similarly to those for the MRT case,however,without explicitly moving into a moment space representation.The corresponding’moments’are derived as left eigenvectors of said collision operator in velocity space.Consequently we can,in a representation independent of the chosen base velocity set,generate the conservation equations.We find a significant degree of freedom in the choice of the collision matrix and the associated basis which leaves the collision operator invariant.We explain why MRT implementations in the literature reproduce identical hydrodynamics despite being based on different orthogonalization relations.More importantly,however,we outline a minimal set of requirements on the moment base necessary to maintain the validity of the hydrodynamic equations.This is particularly useful in the context of position and time-dependent moments such as those used in the context of peculiar velocities and some implementations of fluctuations in a lattice-Boltzmann simulation.展开更多
We analyze the Lattice Boltzmann method for the simulation of fluctuating hydrodynamics by Adhikari et al.[Europhys.Lett.,71(2005),473-479]and find that it shows excellent agreement with theory even for small waveleng...We analyze the Lattice Boltzmann method for the simulation of fluctuating hydrodynamics by Adhikari et al.[Europhys.Lett.,71(2005),473-479]and find that it shows excellent agreement with theory even for small wavelengths as long as a stationary system is considered.This is in contrast to other finite difference and older lattice Boltzmann implementations that show convergence only in the limit of large wavelengths.In particular cross correlators vanish to less than 0.5%.For larger mean velocities,however,Galilean invariance violations manifest themselves.展开更多
文摘A general analysis of the hydrodynamic limit of multi-relaxation time lattice Boltzmann models is presented.We examine multi-relaxation time BGK collision operators that are constructed similarly to those for the MRT case,however,without explicitly moving into a moment space representation.The corresponding’moments’are derived as left eigenvectors of said collision operator in velocity space.Consequently we can,in a representation independent of the chosen base velocity set,generate the conservation equations.We find a significant degree of freedom in the choice of the collision matrix and the associated basis which leaves the collision operator invariant.We explain why MRT implementations in the literature reproduce identical hydrodynamics despite being based on different orthogonalization relations.More importantly,however,we outline a minimal set of requirements on the moment base necessary to maintain the validity of the hydrodynamic equations.This is particularly useful in the context of position and time-dependent moments such as those used in the context of peculiar velocities and some implementations of fluctuations in a lattice-Boltzmann simulation.
文摘We analyze the Lattice Boltzmann method for the simulation of fluctuating hydrodynamics by Adhikari et al.[Europhys.Lett.,71(2005),473-479]and find that it shows excellent agreement with theory even for small wavelengths as long as a stationary system is considered.This is in contrast to other finite difference and older lattice Boltzmann implementations that show convergence only in the limit of large wavelengths.In particular cross correlators vanish to less than 0.5%.For larger mean velocities,however,Galilean invariance violations manifest themselves.
