3 3 RD I A H R C O N G R E S S
Water Engineering
for a Sustainable Environment
www.iahr2009.org
Smoothed Particle
Hydrodynamics
Prof. Joe Monaghan founder of SPH to give Opening Address at the IAHR
Biennial Congress in Vancouver.
In 1977 while on a Sabbatical leave at the University of Cambridge I discussed with
Bob Gingold, then a Post Doctoral Fellow, the possibility of simulating the complex
gas dynamics of star formation by using particles. The idea was to replace the
continuum gas by a set of particles interacting with forces due to the pressure of the
gas and gravity. At that time the only methods available for gas dynamics were finite
difference methods that depended on the system having a simple symmetry.
Because we wanted to explore arbitrary motion
pressure gradients too. The resulting method,
Volcanic eruption in the Bronze Age
we needed something new. I was aware that
which we called Smoothed Particle
Around 1990, after listening to a talk about the
statisticians had used a kernel method to
Hydrodynamics, was extraordinarily flexible. No
Minoan civilization, I got involved with the
estimate probability densities from discrete
grid was required and arbitrary geometry could
archaeology of islands of Santorini and Crete.
information. We found that the same method
be assumed. This method enabled us to inves-
The key question at the time was the extent to
could be used to estimate mass densities,
tigate the problem of the stability of binary
which a pyroclastic flow from a violent volcanic
together with their derivatives, from information
stars, and the fission of a spinning star into two
eruption in the Bronze Age would generate
known only from the particles. If the pressure
stars. The agreement with other methods was
tsunamis on entering the ocean, and whether
was a function of the density we could estimate
excellent especially considering that the
or not the tsunamis could devastate Crete, the
computers were so slow we could only afford
stronghold of the Minoans. I remarked to Peter
low resolution. In those days we began with 40
Bicknell one of the archaeologists at my
particles and after a few years got up to 2000
University, that I thought I could calculate the
but these days 106 to 109 particles are used.
waves generated by a pyroclastic flow entering
The method was extended to handle a wide
the ocean, and asked him if archaeologists
variety of problems in astrophysics amongst
would be interested. He was enthusiastic, and
which are the details of star formation from
referred often to the hard evidence of scientists,
large clouds of gas (Mathew Bate) and the
so I turned to pyroclastic flows and water. The
formation of cosmological structures in the
first stage of this was to tackle problems
evolution of the universe (see for example the
involving the dynamics of water. I took what I
work of Volker Springel). For these problems
thought would be the simplest approach which
SPH is the most powerful known numerical
was to treat water as a slightly compressible
method. The early results and formulation can
fluid with a speed of sound in the fluid very
be found in review articles (Monaghan 1992,
much greater than the speed of the fluid
2005, and Benz 1990).
Prof. Joe Monaghan
motion. The first paper I published on the applications of SPH to incompressible fluids used
this method to simulate dam breaks, bores,
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and wave makers. The results were very good,
features of other rheologies can be recovered
despite the low resolution. We then initiated
at the same time as more complex systems
easy to follow using a particle method. Second,
laboratory experiments to give us information
can be modelled. Typical cases are landslides
SPH provides a natural transition from the
about tsunamis generated by fluid flow,
into water, and dam breaks over granular beds.
tsunamis running onto beaches, and rigid
damage are carried by the matter, and this is
continuum to fragments flying through space
without requiring any change to the code. A
bodies impacting water. I was surprised to find
A different class of problems involves the
finite difference scheme would require a very
that the simulation of a breaking wave was
numerical study of the motion of fish. In its
large number of cells and a very fine resolution
considered difficult because the SPH simula-
simplest form we would like to know the
to follow the fragments through the grid. The
tions were straightforward. The SPH simula-
efficiency of different modes of swimming and
SPH form of the elastic equations is currently
tions were in good agreement with
to do that we have extended SPH to simulate
used for liquid metal forging (see the web site of
experiments. All of this impacted
on studies of Santorini and Crete.
Naturally we used our work, and
planned work, as an excuse to
visit the island of Santorini to
observe the pyroclastic deposits
the Division of Information and Math.
Sciences. of the CSIRO, Australia).
“I believe there is practically no limit to
the computational dynamics problems
we will be able to study effectively”
The final area where SPH provides a
novel technology is in special effects
for movies and videos. Those of you
from the Bronze Age eruption,
who saw the Lord of the Rings
and we formed a team to investigate marine
swimming of linked rigid bodies. With Jules
might like to know that many of the special
deposits on Crete. As the archaeologists
Kajtar I am studying how the motion depends
effects were obtained using SPH. Gollum falling
reminded me, ' nothing can replace the
on the shape of the bodies, their gait, what
into the lava in the last film is an example
personal scrutiny of the site '. Working with
happens when they swim through a free
carried out by the Spanish company Nextl Lmit
archaeologists was very stimulating and there is
surface and how they mix the fluid. We are
whose business is special effects using particle
still much work to be done by scientists inter-
currently exploring the change in motion
methods. Another company is Tweak, which
ested in marine and geophysical problems
produced by covering the bodies with an
used SPH for special effects for a movie called
applied to archaeology.
elastic skin. It is a fascinating field of work with
Charlie and the Chocolate factory, and the
enough problems for a small army of investi-
movie Return of Batman. In these applications
These studies have been taken up by many
gators.
the movie makers are not so much concerned
other authors including Tony Dalrymple at
with high accuracy but rather with realism, and
Johns Hopkins, Damien Violeau at the French
The problem of freezing water
this can be provided by particle methods with
LNHE/EDF ,Andrea Colagrossi at Insean
Particle methods provide a great deal of flexi-
relatively low resolution.
(Rome) and Antonio Souto in Madrid. These
bility because they allow complicated physics
authors have used SPH to extend experimental
to be included easily. Take the problem of
You will see from the examples I have
work on wave impact, fluid flowing through
freezing water. The SPH particles initially have
described that SPH is a versatile method for
complicated conduits, and fluid sloshing in
the properties of the liquid. When they reach
solving difficult problems in computational fluid
tanks carried by ships.
the freezing temperature you keep track of how
dynamics. Combined with new computing
much heat is being extracted and when that
tools, especially the very fast GPUs built origi-
Granicles
reaches the latent heat you give the particle the
nally for the game industry, I believe there is
A problem related to the early work on
properties of ice. The interface between the ice
practically no limit to the computational
pyroclastic flows, is the formation of tsunamis
and the liquid never has to be calculated. It is a
dynamics problems we will be able to study
by landslides. Several authors have used SPH
spin-off from specifying the liquid and ice
effectively.
to study aspects of this problem. It leads the
particles. The geological problem of the motion
simulation of non Newtonian rheologies such as
of lava that solidifies on surfaces exposed to
Prof. Joe Monaghan,
the Bingham rheology (Panizzo, Capone, and
the air, can be computed in the same way.
School of Mathematical Sciences
Monaghan 2008). However, landslides do not
Another fascinating problem is brittle fracture.
Monash University, Australia
satisfy a simple rheology and we are exploring
This was investigated by Benz and Asphaug in
[email protected]
an extension of SPH where the single particles
connection with asteroid collisions, an inevitable
of SPH simulations are replaced by small
process on the way to forming planets, and by
clusters ( typically 5 - 9 particles) which act as a
Monaghan, Gray and Swift in connection with
rigid body. We call these clusters Granicles.
problems involving elastic materials. Their SPH
33rd IAHR Bienial Congress
Vancouver 10-14 August, 2009
These can be combined with fluid SPH
simulations were, and still are, the best available
Keynote Speaker
particles to describe mixtures of rock and
for these problem. For these problems SPH
www.iahr2009.org
water. Our provisional studies show that the
has a number of advantages. First, fracture and
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