HPCI magazine vol.11

Flying with BothWings and Body
– A Supercomputer
Analysis of Butterflies’
Complex Flight
Imagine butterflies fluttering about in a flower garden. Despite their fluttering, joyful appearance,butterflies use very complex movements to generate lift and thrust. Dr. Kosuke Suzuki says, “Themore complex the phenomenon, the more I want to understand it.” He uses numerical simulations
to understand how butterflies fly in the air. Here, we introduce his research, which has a variety ofpotential applications, from Mars exploration to highly efficient refrigerants.

Kosuke Suzuki

Associate Professor, Department of Mechanical Systems Engineering,
Faculty of Engineering, Shinshu University

Calculating the Unique
Flying Style of Butterflies
In order to develop micro air vehicles such asdrones, many studies are being conductedaround the world to understand how flies andmosquitoes fly. “In contrast to these insects,
which do not move their bodies in order to fly,butterflies move their abdomen and thorax (Fig. 1).
In other words, to model the flight of butterflies,
we must account for the movement of not only
their wings, but also their abdomen and thorax. It
is a very complex and challenging study,”
Dr. Suzuki explains.
Butterflies gain lift by flapping their wings downward and thrust by flapping backward. At thattime, the movement of the body is linked to themovement of the wings, and it is believed that01

the angle of the thorax controls the direction the wings move, but the details havenot been clarified.

Immersed Boundary-Lattice
Boltzmann Method (IB-LBM)
with Good Balance of
Accuracy and Computational
Complexity
To understand the flight of a butterfly, it is notenough to simulate the motion of the fluid (air)and the motion of the object (butterfly).
The interaction between the fluid and theobject must also be calculated because theymutually affect each other – when the butterfly
flaps its wings, it induces an air flow, which
affects the motion of the butterfly.
Since he was a graduate student,
D r. Suzuki has been researching methods
to accurately simulate systems in which
the fluid and the object affect each other’s
motion while minimizing the amount ofcomputation needed. There are several
numerical methods for systems in which
the fluid and the object interact (Fig. 2),
and among them, Dr. Suzuki has beendeveloping and improving the “immersedboundary-lattice Boltzmann method(IB-LBM)” (Fig. 2e), which is a combination of the immersed boundary method,which has been known since about 50
years ago, and the lattice Boltzmann
method, which has been rapidly developing in recent years .
The immersed boundary method represents
a moving object in a fluid by applying a force
called a body force around the object (thered area in Fig. 2e). The body force makes
the velocity of the fluid the same as thevelocity of the object's surface, thus preparing a field in which the moving object can beembedded. When applied to the flight of aWings

Fig. 1
AbdomenThorax

HeadBody

A cabbage butterfly
in flight
Captured from a video taken by Dr. Suzuki
and his colleagues. It can be seen that when
the butterfly flaps its wings downward, its
body is flexed and it raises its abdomen
significantly. The wings are raised andlowered 10 times per second while the wings,
abdomen, and thorax move simultaneously.

vol.11 - Flying with Both Wings and Body – A Supercomputer Analysis of Butterflies’ Complex Flight02

obtained by averaging the mass andmomentum of the particles that are
distributed in a space according to the rule
above-mentioned.

butterfly, the butterfly is placed in this field
and is moved according to the equations ofmotion.
On the other hand, the “lattice Boltzmannmethod” is a flow simulation technique thattreats the fluid as a collection of fictitious
particles that can only exist at the intersections of orthogonal lattices (lattice points).
Each particle is assumed to move between
the lattice points at some fixed velocity, andto collide with other particles. The density,
velocity and pressure of the fluid can be

The lattice Boltzmann method, when applied
to incompressible flows such as water andlow-speed air flows, has been mathematically proven to result in the Navier-Stokes equations that describe the motion of fluids. Thelattice Boltzmann method does not require
solving Poisson equation to calculate thepressure, thus allowing for highly accurate

calculations with low computational cost. It isalso suitable for parallel computing becauseit uses only the information of particles on
adjacent lattice points for the calculation of aparticle on one lattice point and does not
require information on faraway particles.
“Both the immersed boundary method andthe lattice Boltzmann method use orthogonallattices, so they are well suited for use incombination. The relative simplicity of thealgorithms and the ease of writing programcode for both are also favorable for research,”(a)Fig. 2

Body

Comparison ofnumerical computing methods
for fluid-object interaction

Fluid
Discretization
Body force
(b)

(c)

(d)

(e)(a)The fluid and the object (body) to becalculated. (b) A method of stepwise
approximation of the space around an object. (c)Boundary-fitted grid method. Creating a gridalong the object. (d) Unstructured grid method.
Using small and large triangles. (e) IB-LBM.
In the methods in (b), (c) and (d), thecomputational load is high because the grid isrecreated each time the object moves. In (e), it is
only necessary to move the body force field, sothe motion of the object can be expressed withthe suppressed computational load.
Suzuki, K.: “Development of an immersed boundary-lattice
Boltzmann method for moving boundary flows and its application
to flapping flight.” NAGARE (Journal of the Japan Society of FluidMechanics) 37 (2018) 215-220.

vol.11 - Flying with Both Wings and Body – A Supercomputer Analysis of Butterflies’ Complex Flight03

Dr. Suzuki says, explaining the advantagesof combining the two methods.

(a) Top-down(b) Bottom-up

Butterfly flight

Dr. Suzuki’s team was the first in the world toapply IB-LBM to butterfly flight in 2012, andin 2013 they succeeded in creating a simulation of a butterfly in flight. “At first, the butterfly did not fly like a real butterfly because it
flipped over or ran in reverse,” Dr. Suzuki
says. “Other researchers are working on
butterfly flight research, but we are the only
team in the world that has solved the equations of motion by linking the motion of thebutterfly, including its body, with the motionof the fluid,” he added proudly.

Simple computationalmodel

MotioncaptureSimulation/Improvement

Computational model
Simulation

Simulation

Two Approaches toUnderstanding Flight“We use two approaches to analysis: top-down
and bottom-up,” Dr. Suzuki explains (Fig. 3).
The top-down approach incorporates theactual movements of butterflies into the computational model. A cabbage butterfly caught
on a riverbank is filmed from three directions
with a high-speed camera, and its shape andmovement are recorded using motion capture.
From this data, a computational model of thebutterfly is created and made to fly in a fluid.
The result is shown in Fig. 3a.

vol.11 - Flying with Both Wings and Body – A Supercomputer Analysis of Butterflies’ Complex Flight

Fig. 3

Butterfly flight as elucidated
by the supercomputer(a) Top-down approach. Butterfly flight was simulatedusing a computational model of a butterfly that faithfully

simulates the shape and behavior of an actual butterfly.
(b) The simulation was performed using a computationalmodel created in the bottom-up approach. The figures in(a) and (b) obtained from the simulations trace the changes in the vortex behind the butterfly.

04

Conversely, the bottom-up approach starts
with a simple model and improves it throughrepeated simulations. First, Dr. Suzuki considered the flight of a simplified model of a butterfly on a computer, consisting of a pair of squarewings and a stick with no thickness. Based on
the results, he examined how factors such as
the shape and mass of the wings affected
the butterfly’s flight, and improved the model
to make it fly more like a butterfly. Fig. 3bshows a simulation of the model he createdin this way.
Comparing the two simulations shown in Fig.
3, the butterfly calculated by the bottom-up
approach flutters in the same way as thebutterfly calculated by the top-down
approach, and a stepped vortex structure
forms behind the wings. The bottom-up
approach also reproduces the butterfly's
movement quite well (Fig. 3b). However,there are still some challenges. There is ahypothesis that butterflies adjust the angle oftheir thorax by moving their abdomen up anddown, but if we include this adjustment in thecalculation using the bottom-up approach,the abdomen swings at an angle that isimpossible in reality. Therefore, in the calculation shown in Fig. 3b, the thorax angle iscalculated by inputting the value obtained
from the experimental data, and the control

vol.11 - Flying with Both Wings and Body – A Supercomputer Analysis of Butterflies’ Complex Flightof the thorax movement by the movement ofthe abdomen is not included in the calculation.
“In the bottom-up approach, our goal is toidentify the minimum elements necessary toreproduce the butterfly's flight as we refine
the model,” Dr. Suzuki says. By bringing thebottom-up and top-down flying manners
closer together, he is trying to elucidate“what is butterfly flight?”
To perform these calculations, Dr. Suzuki
and his team have been using two of HPCI’ssupercomputers, System A (CRAY XC40) at
Kyoto University and the “Flow” Type Isubsystem (FUJITSU FX1000) at Nagoya
University *1. They also use their own computer cluster, but as the number of elements
to be calculated increases, they need thecomputing power and large memory of asupercomputer.
One of the reasons they chose the “Flow” isthat it is compatible with the supercomputer
Fugaku. What kind of calculations would helike to perform if he had the chance to use
the methods developed on Fugaku, which
has enormous computational power? Dr.
Suzuki says, “Currently, in order to reduce
the amount of calculations, we are slightly

lowering the Reynolds number*2 and making
the butterfly’s wings flap more slowly thanthey actually do, but eventually we would liketo do calculations at the actual Reynolds
number. It is also believed that the streaks
and scales on a butterfly’s wings also affectits flight. We do not include these factors inour calculations at this time, but we would
like to include them in our calculations aswell.”Potential Applications
Range from Small Ice Pellets
to Mars Exploration
Dr. Suzuki is also working on applying
IB-LBM to phenomena other than butterfly
flight. One such application is “ice slurry”(tiny ice particles dispersed in water), whichis expected to find use as an excellent refrigerant. “We are applying IB-LBM to calculate
the interaction between ice flow and water
flow, and studying what kind of ice slurry issuitable for efficient heat exchange,” hesays.
Meanwhile, he is also looking to develop hisbutterfly flight research. Micro air vehicles
such as drones that imitate the flight of flies
are not good at recovering their correct
attitude instantly once they lose it. If Dr. Suzuki05

can elucidate a flight model of a butterfly thatrecovers its attitude while swinging its body,he may be able to develop a flying object that
can instantly recover and continue to fly even
if it loses its attitude.

About theResearcher
physics, and majored in aerospace engineering at university. “I wanted to know what

The Martian atmosphere is much less dense
than Earth’s and gives a lower Reynolds
number, so it is difficult to fly on Mars for thefixed-wing aircrafts used on Earth, which aredesigned for high Reynolds number conditions. This is why insect flight is attracting somuch attention. “I would like to develop myresearch and make large-scale calculations
on how to fly in a Mars environment,”
Dr. Suzuki says, expanding on his dreams
for the future.

kind of theory could explain what it means tofly," he says. “I was impressed by the depthof understanding that could be achieved
using fluid engineering, plasma engineering,and electromagnetics," he says. Once hebegan his research, he wanted to unravelcomplex things that could not be explainedby simple fluid engineering, and his application was to flying insects, specifically butterflies. He and his students go to the riverbank
early in the morning to collect cabbage
butterflies sleeping on the underside ofleaves. His hobby is sake tasting. In Nagano,*1 System A (CRAY XC40) was used in FY2021 and the“Flow” Type I subsystem (FUJITSU FX1000) in FY2022.
*2 Reynolds number: Ratio of inertial force to viscous force.
A small value indicates a regular flow (laminar flow),while a large value indicates an irregularly turbulent flow
(turbulent flow).

vol.11 - Flying with Both Wings and Body – A Supercomputer Analysis of Butterflies’ Complex Flight

Dr. Suzuki was fascinated by the shape of

where there are many sake breweries, heinsects and used to collect them in his child-enjoys drinking sake while thinking about thehood. He fell in love with mathematics andbrewer and the production process.

Associated Research Projects
Numerical analysis of flapping flights of insects by IB-LBM using a massive parallel computer(hp210037/hp220037)
Principal Investigator: Kosuke Suzuki, Department of Mechanical Systems Engineering,
Faculty of Engineering, Shinshu University06

vol.11

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https://www.hpci-office.jp/enhttps://fugaku100kei.jp/e/Issued: March 2023