102 JANUARY2020|COMPUTERSHOPPER|ISSUE383
MODELLINGANDSIMULATION
Before we can differentiatethe good from the bad, we need to take
ahigh-level view of the technology.And to do that, we need to
make sure that we’re all singing from the same hymn sheet when
we use two termsthat are sometimes used interchangeably:
modelling and simulation.
Most people would agree that amodel is something that
represents reality.So, forexample,amodel of acar represents areal
car visually.Inthe realm of simulation, amodel still represents
something in the real world, but the representation it captures is its
behaviour,oftenbyusingmathematical equations. This takes us
back to school physics lessons and you’ll probably recall, forexample,
Ohm’s Law,whichiswrittenasV=IR.Putting it intowords, this says
that the potential across aresistor in volts is the value of thatresistor
in ohms, multiplied by the current flowing through it in amps. This,
therefore,isamodel of the behaviour of asimple DC circuit.
Simulation involves using amathematical model to
find out how areal-world system will behave.So, for
example,ifweplugintothe Ohm’s Law equation
afigure of 2amps forIand 3ohms forR,it’s
clear thatVwill be 6volts. What we’ve done,
therefore,istosimulatethat electrical
circuit, although this is asimple example,
which doesn’t need more than abit of
mental arithmetic. In reality,simulation
exercises are much more demanding in
terms of computing power.
Most models of the real world use
differential equations, which define the
rateatwhich some variable changes with time.Now,unlike the
case with Ohm’s Law,however,wecan’t just plug in some numbers
to get an answer.Instead, to calculatethe future stateofasystem
defined by adifferential equation, it’s necessary to progress
through time,calculating the result in astep-by-step fashion.
What’s more,ifyou want accurateresults, you have to step
through in very small increments.
The method of solving adifferential equation is clearly more
taxing than solving Ohm’s Law,but we’re still talking about just a
single equation. In reality,most things we might want to simulate
are defined by lots of differential equations, which are interlinked.
So,for example, today’s models of the atmosphere,whichare used
forweather forecasting, contain at least 10 differential
equations, and often many more.What’s more,they
can’tjustbesolved individually because,inmany
cases, the output of one equation is an input to
another.This represents yet another step up
from the complexity of solving Ohm’s Law –
but we’re not done yet.
So far, we’veseen models that define
how things vary with time.However,most
real-world problems that we might want
to simulatealsovary in space.So, for
example,amodel of the atmosphere has
lots of differential equations that relate,
forexample,towind speeds, pressure and
temperature,but we’re not interested in
just asingle point in the atmosphere.
Instead, we’re interested in weather-related
variables throughout the atmosphere.
ABOVE:Weather forecasting has become farmore accurateinrecent years,
thanks to computer simulations
RIGHT:Formula Studentallows students to design
and competeintheir own racing cars. Simulation is
keytofine-tuning aspects of the design
