An accurate curved boundary treatment in the lattice Boltzmann method
Journal of Computational Physics
Lattice Boltzmann method for 3-D flows with curved boundary
Journal of Computational Physics
Truncation error analysis of lattice Boltzmann methods
Journal of Computational Physics
Analysis of open boundary effects in unsteady lattice Boltzmann simulations
Computers & Mathematics with Applications
Editorial: Mesoscopic methods in engineering and science
Computers & Mathematics with Applications
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The optimal relaxation time of about 0.8090 has been proposed to balance the efficiency, stability, and accuracy at a given lattice size of numerical simulations with lattice Boltzmann methods. The optimal lattice size for a desired Reynolds number can be refined by reducing the Mach number for incompressible flows. The functioned polylogarithm polynomials are defined and used to express the lattice Boltzmann equations at different time scales and to analyze the impact of relaxation times and lattice sizes on truncation errors. Smaller truncation errors can be achieved when relaxation times are greater than 0.5 and less than 1.0. The steady-state lid-driven cavity flow was chosen to validate the code of lattice Boltzmann procedures. The applications of the optimal relaxation parameters numerically balance the stability, efficiency, and accuracy through Hartmann flow. The optimal relaxation time can also be used to select the initial lattice size for the channel flow over a square cylinder with a given Mach number.