Lattice-Boltzmann Solutions with Local Grid Refinement for

Lattice-Boltzmann Solutions with
Local Grid Refinement for Nasal Cavity Flows
Andreas Lintermann
Institute of Aerodynamics and Chair of Fluid Mechanics
RWTH Aachen University
Aachen
Germany
Sonntag, 25. September 2011
Introduction
Anatomy of the nasal cavity:
Examples of pathological cases:
• deformation (rhino-anaplasty)
• malformation
What is the best surgical method for
the individual patient?
missing center
turbinate
missing inferior
turbinate
Flow simulations
support surgical decision process
Sonntag, 25. September 2011
hole in septum
open channel to
paranasal sinus
Lattice-Boltzmann method (LBGK)
•
•
•
Gas-kinetic approach for the simulation of continuum flows
Advantages:
• efficient for the simulation of complex internal flows
• easy automatic grid generation
Solve LBGK-equation iteratively for PPDFs
fi (�x + ξi δt, t + δt) = fi (�x, t) + ωδt · (fieq (�x, t) − fi (�x, t))
D3Q19 model:
•
Solve TLBGK-equation to obtain temperature distribution
gi (�x + ξi δt, t + δt) = gi (�x, t) + Ωg · (gieq (�x, t) − gi (�x, t))
Sonntag, 25. September 2011
Local grid refinement (Hänel etc.)
•
•
Overlay of cells from different levels are required
Reconstruction required:
• obtain macroscopic variables by bi- or tri-linear interpolation
bx f
bxc
available PPDFs on both levels
missing PPDFs from different level
O. Filippova and D. Hänel. Boundary-Fitting and Local Grid Refinement for Lattice-BGK Models.
International Journal of Modern Physics C, 9:1271–1279, 1998.
A. Dupuis and B. Chopard. Theory and applications of an alternative lattice Boltzmann grid refinement algorithm.
Phys. Rev. E, Volume 67(6):066707, Jun 2003.
Sonntag, 25. September 2011
Nasal cavity flows
•
•
Application: Flow in a nasal cavity
Re = 710 based on 125 ml/sec per
averaged nostril
septum
paranasal sinus
right nostril
left nostril
lower turbinate
throat
right nostril
throat
Sonntag, 25. September 2011
left nostril
throat
Nasal cavity flows
•
no levels
no cells
reduction
time/it.
•
Grid refinement:
Gs
1
4.744 × 107
0.0%
0.255s
Gm2
2
4.335 × 107
8.6%
0.324s
Gm3
3
2.277 × 107
52.0%
0.186s
Temperature distribution (inflow: 20°C, wall 37°C)
heating capability: 13°C increase
right nostril
throat
Sonntag, 25. September 2011
left nostril
throat
Scalability and future work
ideal speedup
0.262 x 106 cells/core
1.4
1.2
speedup
1
0.8
0.6
0.4
0.2
0
1024
•
•
2048
3072
number of cores
4096
Scale-up tests on BlueGene System JUGENE at FZ Jülich
good scalabilty
9
Maximal number of cells so far: 1.074 × 10
future simulations will require a massive amount of cells
Sonntag, 25. September 2011
Scalability and future work
•
•
Scale-up tests on BlueGene System JUGENE at FZ Jülich
good scalabilty
9
Maximal number of cells so far: 1.074 × 10
future simulations will require a massive amount of cells
simulations of the complete respiratory system
Sonntag, 25. September 2011
Conclusion
•
Analysis of the flow in the nasal cavity based on
•
•
•
streamline characteristics
backflow and vortex characteristics
Local grid refinement:
52.0% reduction for three levels
more efficient computation
•
Heat convection / diffusion allows analysis of heating capability
•
Fast and easy mesh generation with a Cartesian grid generator
•
Good scalability and well suited for Massive Parallel Computing
efficient tool to simulate flows in highly intricate geometries
Sonntag, 25. September 2011
Thank you for your attention
Sonntag, 25. September 2011