Copyright © A. Filippone (1996-2001). All Rights Reserved.

Computational Aerodynamics

Boltzmann Gas Lattice

The Boltzmann Gas Lattice Method (BGLM) models directly the physics of the fluid particles and achieves the same results as the Navier-Stokes equations, that are a continuum representation of the fluid dynamics.

The representation of the dynamics of all the particles with the BGLM is practically very expensive, therefore some simplification is used at the microscopic level.

The particles are described in terms of velocity components in the time-domain, in elementary cartesian volume units (lattices). Particles move, collide and eventually fall into another lattice. The full description of this dynamics is accomplished through the conservation of mass, momentum and energy.

The idea behind the method is to solve indirectly the equations for the continuum (Navier-Stokes) by mimicking the fluid dynamics at the molecular level.

There are two well known lattice-based methods: Lattice Gas Automata and the Lattice Boltzmann method.

Gas Automata Methods

These methods are based on very simple particle dynamics that allow only a single particle of a specified velocity and direction to be on a given lattice. The number of possible states for a given particle is 12 (6 directions, 1 or 2 lattices per time step). Therefore a particular lattice site can be represented with 12 bits.

The movement and collision of particles in this system can be computed with integer arithmetic. Mass, momentum, and energy are intrincsically conserved and the computation is unconditionally stable.

Lattice Boltzmann Methods

These methods replace the integer particle populations with floating point numbers. The number of bits required is at least 32, therefore they require large computer power. The conservation of mass, momentum, and energy is now limited by the precision of floating point errors, which lead to stability problems.

Selected References

  • Rothman DH, Zaleski S. Lattice-Gas Cellular Automata, Cambridge Univ. Press, Cambridge 1997.

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Copyright © A. Filippone (1996-2001). All Rights Reserved.