1. Lattice Boltzmann Simulation of Fluid Flows M.J. Pattison & S. Banerjee MetaHeuristics LLC Santa Barbara, CA 93105

2. Main Topics Objectives Lattice Boltzmann method Complex geometry Multicomponent flow Turbulence modelling Parallelisation

3. Objectives – Phase 1 NSTX Lithium Free Surface Module (ORNL) Complex geometry Multiphase flow Heat transport Turbulence Fluid-wall interactions Parallelisation capability

4. Objectives – Phase II MHD Chemical reactions Parallel code Input/output processing

5. Lattice Boltzmann Method Solve for velocity distribution is a relaxation time (function of viscosity) a is force term

6. Projection Method 1. 2. 3. Predictor Poisson eqn Corrector Poisson equation is elliptic. Can solve using spectral method (FFT) for simple geometry or by iterative method. Methods use non-local data so making parallel processing less efficient.

7. Capabilities of LB code Can handle complex geometry easily Multicomponent/multiphase flows Turbulence models – LES or algebraic Well suited to parallel processing – almost linear scaling with number of CPUs

8. Complex Geometry a b Fluid Wall No need for body-fitted grid but need distributions at point b is function of distance from wall is an equilibrium distribution

9. Flow over Cylinder

10. Backward Facing Step Velocity profiles downstream of step. Left at x/S = 6, right at at x/S = 20

11. Multicomponent Flows Model interactions between components using a force term Where summation is over nearest neighbours and the different components. is a function of density Can model effects of: - surface tension - phase change (i.e. condensation) - immiscible fluids

12. Movement of Droplet down Wall Drop is initially semi-circular, with surrounding fluid stationary Drop spreads due to surface tension, then moves down wall

13. Penetration of Dense Fluid into Light Fluid

14. Turbulence Modelling Use Baldwin-Lomax algebraic model Smagorinski type LES model Models use an “eddy viscosity” to account for effects of turbulence Both models only require local data, so are suited for parallel processing

15. Turbulence in Shear Flow

16. Parallelisation Split domain up into slabs or blocks Assign each one to a different processor Speed of computation for different numbers of CPUs used – plane Poiseuille flow problem

17. Conclusions 3-D transient Lattice Boltzmann code with following capabilities developed: Multicomponent flow Complex geometry Turbulence modelling Efficient parallel processing with almost linear scaling

18. NSTX Lithium Free Surface Module (ORNL)