Lattice Boltzmann methods

In the lattice Boltzmann method (also known lattice Boltzmann method, or lattice -Boltzmann method) is a late 1980s developed method for the numerical flow simulation. The phase space is as the name suggests discretized for the numerical solution of the Boltzmann equation by a grid. By incorporating other models, other physical processes, such as thermodynamic processes in fluids or solids by means of Lattice Boltzmann methods can be calculated in a continuum.

The Lattice -Boltzmann method is based on the calculation of a simplified micro - particles dynamics. That is, there is performed a simulation on the particle level. Due to the internal structure (low memory and computational requirements per cell), the process is, among other things for the calculation of flows in complex geometries. The Lattice -Boltzmann method has its theoretical basis in statistical physics. The interaction of the microscopic particles is described by the Boltzmann equation.

Graphic Organizer of the algorithm

In order to solve the Boltzmann equation it is discretized. The discretization is achieved by inserting a grid in real space, which the velocities are discretized. Thus, the whole phase space is discretized. In popular images represent the Points in position space, while the arrows represent how likely the velocity of the particles (which are associated with a point ) occurs in the direction of the arrow at each point.

The algorithm consists in the simplest case of two sub- steps ( the order fixed, but is arbitrary ):

All arrows are clearly shifted to the next grid point ( according to their direction) while streaming. In the collision step, the collision rules are applied. These rules must be given the mass and the momentum.

Software

  • Palabos: Free (GPL ), highly scalable framework for LBM simulations
  • Power Flow: commercial CFD code, based on LBM
  • XFlow: commercial CFD code, based on LBM
  • OpenLB is a free CFD software (GPL ), based on LBM, C
  • El'Beem is a free LBM -based CFD software (GPL ) which may also be involved in the Blender 3D graphics software for the simulation of fluids.
500422
de