simulating the swimming of microorganisms towards swarming · simulating the swimming of...
TRANSCRIPT
![Page 1: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/1.jpg)
Simulating the Swimming ofMicroorganisms towards Swarming
K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U. Rüdea,b
DSFD 2014, Paris, FranceaLehrstuhl für Informatik 10 (Systemsimulation), FAU Erlangen-NürnbergbCluster of Excellence: Engineering of Advanced Materials, FAU Erlangen-NürnbergcInstitut für Theoretische Physik I, FAU Erlangen-Nürnberg
![Page 2: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/2.jpg)
Flow Regimes
104
109
102
10-4
Re
∗all images taken from www.wikipedia.com
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 2
![Page 3: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/3.jpg)
Flow at Low Reynolds Number: Purcell’s Scallop Theorem∗
t2
t1
t
xx1
x2
Stokes flow
• domination of viscous forces• small momentum• always laminar• time reversible• no coasting⇒ we need asymmetric, non-time
reversible motion to achieve anynet movement
∗E.M. Purcell. Life at low Reynolds number. American Journal of Physics 45: 3-11 (1977)
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 3
![Page 4: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/4.jpg)
Overall Goal: Simulation of a Swarm
Characteristics of a Swarm
• large-scale collective hydrodynamics• complex long-time dynamics• pattern formation
⇒ we want to study these effects⇒ compare analytical calculations with simulations⇒ not only of a single swimmer but many of them
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 4
![Page 5: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/5.jpg)
Ingredients for a Simulation of a Swarm
“Physics” Ingredients
• model of a swimmer• non-time reversible cycling strategy
“Software” Ingredients
• fluid and rigid body simulation tool• coupling both tools consistently• allow for large scale computations
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 5
![Page 6: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/6.jpg)
Ingredients for a Simulation of a Swarm
“Physics” Ingredients
% model of a swimmer• non-time reversible cycling strategy
“Software” Ingredients
• fluid and rigid body simulation tool• coupling both tools consistently• allow for large scale computations
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 6
![Page 7: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/7.jpg)
Physical Model of a Swimmer
• we choose the simplest possible design:Golestanian’s* swimmer
• connections between the objects:• linear spring-damper systems†
• angular spring-damper systems‡
∗A. Najafi and R. Golestanian. Simple swimmer at low Reynolds number: Three linked spheres. Phys. Rev. E, 69(6):062901 (2004)†K. Pickl et al. All good things come in threes – three beads learn to swim with lattice Boltzmann and a rigid body solver. JoCS 3(5):374 – 387 (2012)‡K. Pickl et al. Parallel Simulations of Self-propelled Microorganisms. Advances in Parallel Computing, Vol. 25 (2014)DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 7
![Page 8: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/8.jpg)
Ingredients for a Simulation of a Swarm
“Physics” Ingredients
! model of a swimmer% non-time reversible cycling strategy
“Software” Ingredients
• fluid and rigid body simulation tool• coupling both tools consistently• allow for large scale computations
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 8
![Page 9: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/9.jpg)
Non-time Reversible Cycling Strategy
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000Time step
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
Forc
e (x
-com
ponen
t)
Force on body 2
Force on body 1
Force on body 3
• total applied force vanishes over one cycle (displacement ofswimmer over one cycle is zero in absence of fluid)
• applied along specified main axis of swimmer on center of massof each body (in this case: x-direction)
• net driving force acting on system at each instant of time is zero
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 9
![Page 10: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/10.jpg)
Ingredients for a Simulation of a Swarm
“Physics” Ingredients
! model of a swimmer! non-time reversible cycling strategy
“Software” Ingredients
% fluid and rigid body simulation tool• coupling both tools consistently• allow for large scale computations
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 10
![Page 11: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/11.jpg)
Software
Fluid Simulation – WALBERLA
(widely applicable Lattice Boltzmann solver from Erlangen)
• suited for various flow applications• different fluid models (SRT, TRT∗, MRT)• suitable for homo- and heterogeneous architectures• large-scale, MPI-based parallelization
Rigid Body Simulation – pe• based on Newton’s mechanics• fully resolved objects (sphere, box, . . . )• connections between objects can be soft or hard constraints• accurate handling of friction during collision†
• large-scale, MPI-based parallelization
∗I. Ginzburg et al. Two-relaxation-time lattice Boltzmann scheme: About parametrization, . . . . Comm. in Computational Physics, 3(2):427–478, (2008)†P. A. Cundall and O. D. L. Strack. A discrete numerical model for granular assemblies. Geotechnique, 29:47–65, (1979)DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 11
![Page 12: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/12.jpg)
Ingredients for a Simulation of a Swarm
“Physics” Ingredients
! model of a swimmer! non-time reversible cycling strategy
“Software” Ingredients
! fluid and rigid body simulation tool% coupling both tools consistently• allow for large scale computations
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 12
![Page 13: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/13.jpg)
Coupling both Frameworks: Four-Way Coupling
1. Object Mapping2. LBM Communication3. Boundary Handling
(including Hydrodynamic Forces)
4. Stream Collide5. Lubrication Correction
6. Physics Engine
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 13
![Page 14: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/14.jpg)
Ingredients for a Simulation of a Swarm
“Physics” Ingredients
! model of a swimmer! non-time reversible cycling strategy
“Software” Ingredients
! fluid and rigid body simulation tool! coupling both tools consistently% allow for large scale computations
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 14
![Page 15: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/15.jpg)
Allow for Large Scale Computations
Parallel Discrete Element Method (DEM)∗
• handling of pair-wise spring-like interactions, extending not only overneighboring but also over multiple process domains
• for long-range interactions: only associated processes communicate
∗K. Pickl et al. Parallel Simulations of Self-propelled Microorganisms. Advances in Parallel Computing, Vol. 25 (2014)∗M. Hofmann. Parallelisation of Swimmer Models for Swarms of Bacteria in the Physics Engine pe. Master’s thesis, LSS, FAU Erlangen-Nürnberg (2013)
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 15
![Page 16: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/16.jpg)
Allow for Large Scale ComputationsWeak Scaling Results on JUQUEEN∗
largest simulated setup:
131,072 cores
16,777,216 swimmers!
not displayed: Setup, Swimmer Setup and Lubrication Correction∗K. Pickl et al. Parallel Simulations of Self-propelled Microorganisms. Advances in Parallel Computing, Vol. 25 (2014)
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 16
![Page 17: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/17.jpg)
Ingredients for a Simulation of a Swarm
“Physics” Ingredients
! model of a swimmer! non-time reversible cycling strategy
“Software” Ingredients
! fluid and rigid body simulation tool! coupling both tools consistently! allow for large scale computations
We have all necessary ingredients forthe simulation of a swarm!
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 17
![Page 18: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/18.jpg)
Ingredients for a Simulation of a Swarm
“Physics” Ingredients
! model of a swimmer! non-time reversible cycling strategy
“Software” Ingredients
! fluid and rigid body simulation tool! coupling both tools consistently! allow for large scale computations
We have all necessary ingredients forthe simulation of a swarm!
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 17
![Page 19: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/19.jpg)
Initial Configuration of the System
• characteristics of the fluid simulationviscosity 73.6 · 10−6 m 2/sresolution dx 1.0 · 10−6mrelaxation time 1.5
• characteristics of the channeldimensions 400× 200× 200 lattice cellsswimming direction along x-axisall boundaries free slip
• characteristics of the external forcespulse length 4692 time stepsphase shift π/2
• geometric characteristics of the swimmer
radius of spheres 4 lattice cellsmass of spheres 400 on the latticerest length 16 lattice cells
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 18
![Page 20: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/20.jpg)
Oscillations of the Arms
0 4000 8000 12000 16000 20000 24000 28000 32000Time step
4
5
6
7
8
9
10
11
12
13
Dis
tan
ce [
latt
ice
cell
s]Leading Arm
Trailing Arm
⇒ leading arm is the dominating arm in terms of collisions⇒ system is in a steady state after 5 cycles
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 19
![Page 21: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/21.jpg)
Results of the Initial System
1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6
Amplitude [10-5N]
0.0
0.5
1
1.5
2.0
2.5
3.0
3.5
Sw
imm
er V
elo
city
[10
-4]
amplitude 1.0 · 10−5 N
swimming velocity 0.515 · 10−4
distance in 1 cycle 0.25RE swimmer 0.00618
amplitude 2.6 · 10−5 N
swimming velocity 3.176 · 10−4
distance in 1 cycle 1.56RE swimmer 0.03811
*all other quantities given on the lattice
⇒ explore bounds of low RE⇒ maximize swimming velocity
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 20
![Page 22: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/22.jpg)
Tuning the Swimmer Speed by Changing its Geometry
• characteristics of the fluid simulationviscosity 73.6 · 10−6 m 2/sresolution dx 1.0 · 10−6mrelaxation time 1.5
• characteristics of the channeldimensions 400× 200× 200 lattice cellsswimming direction along x-axisall boundaries free slip
• characteristics of the external forcespulse length 4692 time stepsphase shift π/2
• geometric characteristics of the swimmer
radius of spheres 4 lattice cellsmass of spheres 400 on the latticerest length 16
• resulting configurations
radiusrest length
channel dimensions(4∗radius)
4 16 400× 200× 2006 24 420× 204× 2048 32 440× 208× 208
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 21
![Page 23: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/23.jpg)
Tuning the Swimmer Speed by Changing its Geometry
• characteristics of the fluid simulationviscosity 73.6 · 10−6 m 2/sresolution dx 1.0 · 10−6mrelaxation time 1.5
• characteristics of the channeldimensions 400× 200× 200 lattice cellsswimming direction along x-axisall boundaries free slip
• characteristics of the external forcespulse length 4692 time stepsphase shift π/2
• geometric characteristics of the swimmer
radius of spheres 4 lattice cellsmass of spheres 400 on the latticerest length 16
• resulting configurations
radiusrest length
channel dimensions(4∗radius)
4 16 400× 200× 2006 24 420× 204× 2048 32 440× 208× 208
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 21
![Page 24: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/24.jpg)
Tuning the Swimmer Speed by Changing its Geometry
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
Amplitude [10-5N]
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
Sw
imm
er V
elo
city
[10
-4]
Rest length 16, R4, tau 1.5
Rest length 24, R6, tau 1.5
Rest length 32, R8, tau 1.5
radius 4, rest length 16
max. amplitude 2.6 · 10−5 Nswimming velocity 3.176 · 10−4
distance in 1 cycle 1.56RE swimmer 0.03811
radius 6, rest length 24
max. amplitude 4.5 · 10−5 Nswimming velocity 4.228 · 10−4
distance in 1 cycle 2.08RE swimmer 0.07611
radius 8, rest length 32
max. amplitude 6.7 · 10−5 Nswimming velocity 4.734 · 10−4
distance in 1 cycle 2.33RE swimmer 0.11363
*all other quantities given on the lattice
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 22
![Page 25: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/25.jpg)
So far...
• we have a distance gain from 0.25 to 2.33 lattice cells per cycle• we have a velocity gain from 0.515 · 10−4 to 4.734 · 10−4
• and have reached a RE of 0.11363 (compared to 0.00618)
Can we go any faster?• rest length 32 lattice cells and radius 8 lattice cells→ swimmer x-size of 80 lattice cells⇒ we do not want to enlarge this any further!
• rest length 32 lattice cells and radius 6 lattice cells→ still sufficiently resolved→ allows for more oscillations of the arms
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 23
![Page 26: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/26.jpg)
So far...
• we have a distance gain from 0.25 to 2.33 lattice cells per cycle• we have a velocity gain from 0.515 · 10−4 to 4.734 · 10−4
• and have reached a RE of 0.11363 (compared to 0.00618)
Can we go any faster?
• rest length 32 lattice cells and radius 8 lattice cells→ swimmer x-size of 80 lattice cells⇒ we do not want to enlarge this any further!
• rest length 32 lattice cells and radius 6 lattice cells→ still sufficiently resolved→ allows for more oscillations of the arms
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 23
![Page 27: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/27.jpg)
So far...
• we have a distance gain from 0.25 to 2.33 lattice cells per cycle• we have a velocity gain from 0.515 · 10−4 to 4.734 · 10−4
• and have reached a RE of 0.11363 (compared to 0.00618)
Can we go any faster?• rest length 32 lattice cells and radius 8 lattice cells→ swimmer x-size of 80 lattice cells⇒ we do not want to enlarge this any further!
• rest length 32 lattice cells and radius 6 lattice cells→ still sufficiently resolved→ allows for more oscillations of the arms
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 23
![Page 28: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/28.jpg)
So far...
• we have a distance gain from 0.25 to 2.33 lattice cells per cycle• we have a velocity gain from 0.515 · 10−4 to 4.734 · 10−4
• and have reached a RE of 0.11363 (compared to 0.00618)
Can we go any faster?• rest length 32 lattice cells and radius 8 lattice cells→ swimmer x-size of 80 lattice cells⇒ we do not want to enlarge this any further!
• rest length 32 lattice cells and radius 6 lattice cells→ still sufficiently resolved→ allows for more oscillations of the arms
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 23
![Page 29: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/29.jpg)
Maximizing the Oscillations of the Arms
3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
Amplitude [10-5N]
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
Sw
imm
er V
eloci
ty [
10
-4]
Rest length 24, R6, tau 1.5
Rest length 32, R6, tau 1.5
Rest length 32, R8, tau 1.5radius 8, rest length 32
max. amplitude 6.7 · 10−5 Nswimming velocity 4.734 · 10−4
distance in 1 cycle 2.33RE swimmer 0.11363
radius 6, rest length 32
max. amplitude 7.0 · 10−5 Nswimming velocity 7.731 · 10−4
distance in 1 cycle 3.81RE swimmer 0.17627
*all other quantities given on the lattice
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 24
![Page 30: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/30.jpg)
Conclusions of the Geometry Study
• we have a final distance gain from 0.25 to 3.81 lattice cells per cycle• we have a final velocity gain from 5.15 · 10−4 to 7.731 · 10−4
• and have eventually reached a RE of 0.17627 (compared to 0.00618)
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 25
![Page 31: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/31.jpg)
Changing the Viscosity of the Fluid
• characteristics of the fluid simulationviscosity 73.6 · 10−5 m 2/sresolution dx 10−6mrelaxation time 10
• characteristics of the channeldimensions 400× 200× 200 lattice cellsswimming direction along x-axisall boundaries free slip
• characteristics of the external forcespulse length 4932 time stepsphase shift π/2
• geometric characteristics of the swimmer
radius of spheres 4 lattice cellsmass of spheres 400 on the latticerest length 16 lattice cells
⇒ compare with our initial system⇒ with higher viscosity theory predicts
slower swimmer in this regime
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 26
![Page 32: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/32.jpg)
Changing the Viscosity of the Fluid
• characteristics of the fluid simulationviscosity 73.6 · 10−5 m 2/sresolution dx 10−6mrelaxation time 10
• characteristics of the channeldimensions 400× 200× 200 lattice cellsswimming direction along x-axisall boundaries free slip
• characteristics of the external forcespulse length 4932 time stepsphase shift π/2
• geometric characteristics of the swimmer
radius of spheres 4 lattice cellsmass of spheres 400 on the latticerest length 16 lattice cells
⇒ compare with our initial system⇒ with higher viscosity theory predicts
slower swimmer in this regime
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 26
![Page 33: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/33.jpg)
Oscillations of the two Arms
0 15000 30000 45000 60000 75000 90000 105000 120000Time step
7.5
7.75
8
8.25
8.5
8.75
9
Dis
tan
ce [
latt
ice
cell
s]Leading Arm
Trailing Arm
⇒ leading arm is still the dominating arm in terms of collisions⇒ system is not in a steady state after 5 cycles but after 10 cycles⇒ after switching off the external forces, it takes longer for the springs to relaxDSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 27
![Page 34: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/34.jpg)
Comparing Viscosities
at amplitude 1.0 · 10−5 N:
viscosity 73.6 · 10−6 m 2/s
swimming velocity 8.6276 · 10−7
distance in 1 cycle 0.25RE swimmer 0.00618
viscosity 73.6 · 10−5 m 2/s
swimming velocity 5.1523 · 10−5
distance in 1 cycle 0.0043615RE swimmer 0.00001
*all other quantities given on the lattice
⇒ quantitative agreement isobtained at low RE and smalloscillations, where actually isthe limit of the theory
1.0 2.0 3.0 4.0
Amplitude [10-5N]
0.0
1.0
2.0
3.0
4.0
5.0
Sw
imm
er V
eloci
ty [
10
-4]
Simulation: nu = 73.6.10-6 m 2/s
Theory: nu = 73.6.10-6 m 2/s
Simulation: nu = 73.6.10-5 m 2/s
Theory: nu = 73.6.10-5 m 2/s
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 28
![Page 35: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/35.jpg)
Comparing Viscosities
at amplitude 1.0 · 10−5 N:
viscosity 73.6 · 10−6 m 2/s
swimming velocity 8.6276 · 10−7
distance in 1 cycle 0.25RE swimmer 0.00618
viscosity 73.6 · 10−5 m 2/s
swimming velocity 5.1523 · 10−5
distance in 1 cycle 0.0043615RE swimmer 0.00001
*all other quantities given on the lattice
⇒ quantitative agreement isobtained at low RE and smalloscillations, where actually isthe limit of the theory
1.0 2.0 3.0 4.0
Amplitude [10-5N]
0.0
1.0
2.0
3.0
4.0
5.0
Sw
imm
er V
eloci
ty [
10
-4]
Simulation: nu = 73.6.10-6 m 2/s
Theory: nu = 73.6.10-6 m 2/s
Simulation: nu = 73.6.10-5 m 2/s
Theory: nu = 73.6.10-5 m 2/s
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 28
![Page 36: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/36.jpg)
Comparing Viscosities
at amplitude 1.0 · 10−5 N:
viscosity 73.6 · 10−6 m 2/s
swimming velocity 8.6276 · 10−7
distance in 1 cycle 0.25RE swimmer 0.00618
viscosity 73.6 · 10−5 m 2/s
swimming velocity 5.1523 · 10−5
distance in 1 cycle 0.0043615RE swimmer 0.00001
*all other quantities given on the lattice
⇒ quantitative agreement isobtained at low RE and smalloscillations, where actually isthe limit of the theory
1.0 2.0 3.0 4.0
Amplitude [10-5N]
0.0
1.0
2.0
3.0
4.0
5.0
Sw
imm
er V
eloci
ty [
10
-4]
Simulation: nu = 73.6.10-6 m 2/s
Theory: nu = 73.6.10-6 m 2/s
Simulation: nu = 73.6.10-5 m 2/s
Theory: nu = 73.6.10-5 m 2/s
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 28
![Page 37: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/37.jpg)
Conclusions and Future Work
Conclusions• successfully achieved a higher swimming
velocity by changing the swimmer geometry• obtained quantitative agreement of the
viscosity dependence within one regime
• demonstrate flexibility of our framework byseveral parameter studies
Future Work• static grid refinement→ reflect infinite domain as good as possible
• analyze collective behavior of swimmerssystematically
• improvement of parallel I/O and associateddata analysis
*images courtesy of F. Schornbaum, E. Fattahi: “A Study of the Vocal Fold”
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 29
![Page 38: Simulating the Swimming of Microorganisms towards Swarming · Simulating the Swimming of Microorganisms towards Swarming K. Pickl a,b J. Pande b,c H. Köstler a A.-S. Smithb,c U](https://reader033.vdocuments.us/reader033/viewer/2022060223/5f07c5997e708231d41eaa62/html5/thumbnails/38.jpg)
Thank you for your attention!Extract from the References• K. Pickl et al. Parallel Simulations of Self-propelled Microorganisms. Advances in Parallel Computing,
Vol. 25 (2014)• K. Pickl et al. All good things come in threes – three beads learn to swim with lattice Boltzmann and a
rigid body solver. Journal of Computational Science, 3(5):374 – 387, 2012.• C. Godenschwager et al. A Framework for Hybrid Parallel Flow Simulations with a Trillion Cells in
Complex Geometries. Proceedings of SC13: International Conference for High PerformanceComputing, Networking, Storage and Analysis. p. 35-1 – 35-12.
• A. Najafi and R. Golestanian. Simple swimmer at low Reynolds number: Three linked spheres. Phys.Rev. E, 69(6):062901, 2004.
• C. M. Pooley et al. Hydrodynamic interaction between two swimmers at low Reynolds number. Phys.Rev. Lett., 99:228103, 2007.
• D. Saintillan and M. J. Shelley. Instabilities and Pattern Formation in Active Particle Suspensions:Kinetic Theory and Continuum Simulations. Phys. Rev. Lett., 100:178103, 2008.
Acknowledgments
DSFD 2014 | [email protected] | FAU Erlangen-Nürnberg | Simulating the Swimming of Microorganisms towards Swarming 30