### Project Description

**Preconditioned Navier-Stokes Schemes from the Generalised Lattice Boltzmann Equation**

by

Izquierdo, S.; Fueyo, N.

in

Computational Fluid Dynamics. 2008

### Abstract

Preconditioning of Navier-Stokes equations is a widely used technique to

speed up Computational Fluid Dynamics simulations of steady flows. In this work

a systematic study is performed of time-derivative preconditioners of Navier-Stokes

equations that can be derived from the generalized lattice Boltzmann equation. In this

way, lattice Boltzmann models equivalent to preconditioned Navier-Stokes systems are

constructed, and it becomes possible to take advantage of the knowledge generated

in this field to improve the convergence to steady state of lattice-Boltzmann flowcalculations.

The generalized lattice Boltzmann equation presents a number of tunable

parameters, which provide access to a generalized hydrodynamics. Starting from this

fully parametrized lattice Boltzmann scheme, and applying restrictions to account for

isotropy and Galilean invariance, the number of free parameters is initially reduced.

Then, with the aid of Chapman-Enskog procedure, the recovery of the Navier-Stokes

equations requires a further reduction in the number of parameters. With the final

number of free parameters, and an additional re-scaling of momentum, two different

preconditioners are obtained, which are studied according to its condition number and

compared with typical Navier-Stokes preconditioners.