The Lattice-Boltzmann Method on Optimal Sampling Lattices
Simulations of an incompressible fluid via the Lattice-Boltzmann method (LBM) are usually performed on a Cartesian lattice. In this project, we demonstrate that the body-centered cubic (BCC) lattice is better suited for such simulations and yields a 30% saving in the number of samples without incurring any loss in accuracy. We extend the single relaxation time Lattice Boltzmann Method (LBM) to the three-dimensional body-centered cubic (BCC) lattice. We show that the D3bQ15 lattice defined by a fifteen neighborhood connectivity of the BCC lattice is not only capable of more accurately discretizing the velocity space of the continuous Boltzmann equation as compared to the D3Q15 Cartesian lattice, it also achieves a comparable spatial discretization with 30% less samples. We validate the accuracy of our proposed lattice by investigating its performance on the 3D lid-driven cavity flow problem. We quantitatively compare our results with published benchmark data and show that the D3bQ15 lattice offers significant cost savings while maintaining a comparable accuracy. We use a scalar dye advection method to visualize the flow fields, taking advantage of the fact that volumetric data on BCC lattices can be rendered faster than Cartesian lattices.