Lattice Boltzmann Method

In Lattice Boltzmann Method (LBM), fictitious particles resembling groups of molecules are considered in a lattice with a finite set of velocities. These particles collide at the lattice nodes and propagate in such a way that the Navier-Stokes hydrodynamics is recovered in the macroscopic limit.

At SankhyaSutra Labs, we use Entropic Lattice Boltzmann formulations for hydrodynamics, which is inherently stable. Entropic LBM does not require empirical modelling approaches, such as Reynolds Average Navier-Stokes (RANS) approach for turbulent flow. The accuracy of Entropic LBM is similar to Large Eddy Simulation (LES) for low resolution and smoothly approaches the accuracy level of Direct Numerical Simulation (DNS) as resolution is increased. 

Being inherently parallelizable, LBM scales almost linearly with the available compute power. In other words, there is no inherent limitation on the size of the problem that can be accurately simulated given adequate computational resources.

Conventional LBM implementations use simple cubic (SC) lattice, which require grid refinement near solid boundaries or in zones of flow variations. Another innovative feature of Sankhyasutra’s technology is the use of Crystallographic LBM, where body centred cubic (BCC) lattice is used instead of SC lattice. BCC lattice captures geometry better than SC lattice with a given number of lattice points improving accuracy.

Lattice Boltzmann Method (LBM)
Simple Cubic mesh used in Lattice Boltzmann Method
Simple Cubic (SC) Mesh Lattice Boltzmann Method
Body Centred Cubic mesh used in Entopic Lattice Boltzmann Method
Body Centred Cubic (BCC) Mesh Lattice Boltzmann Method