Higher order Galilean invariant Lattice Boltzmann method

• Main Author: Wahyu Perdana Yudistiawan
• Other Authors: Santosh Ansumali
• Format: Theses and Dissertations
• Language: English
• Published: 2013
• Subjects: DRNTU::Engineering::Computer science and engineering::Computing methodologies::Simulation and modeling; DRNTU::Science::Mathematics::Applied mathematics::Simulation and modeling
• Online Access: https://hdl.handle.net/10356/53514
• Institution: Nanyang Technological University

With the increase of microfluidics applications in recent years, there has been more emphasis given to find alternative modeling method in the microflow regime where the classical Navier-Stokes model broke down. In this regime, the mean-free path of a particle is comparable to the characteristic size of the channel, giving the boundary interaction a major role to play. While methods such as molecular dynamics and Monte-Carlo are excellent for simulating transitional regime, the computational cost is too expensive to be used for any realistic simulation in near continuum sub-sonic regime. In recent years, Lattice Boltzmann models are gaining traction as a robust method for simulations in the transitional microflow regime, filling the gap between the Navier-Stokes based solver and molecular dynamics. In this thesis, we present a systematic optimization of the standard Lattice Boltzmann (LB) models. The analytical study of D2Q9 model is elaborated for simple channel flow and the results are compared with slip flow solution by Cercignani giving a benchmark of LB performance. We then introduce a scheme to reduce the number of velocities of higher order models using renormalization method, projecting D2Q16 model back to a modified D2Q9 model while maintaining the same analytical solution. In this manner, we manage to construct a modified D2Q9 model that capable of reproducing Knudsen layer in the velocity profile. Lastly, we introduce a novel scheme which gives additional degree of freedom for the same number of discrete velocities in three-dimension, in particular we discuss the application of the scheme on D3Q27 model. We show the existence of an off-lattice D3Q27 model with correct equilibrium to recover Galilean invariant form of Navier-Stokes equation, which exhibit better accuracy and excellent velocity profile that match the result from classical Grad 13-moments model.