To simulate a phenomenon, on a computer or otherwise, we need a mathematical model that imitates the phenomenon. Such a model can be obtained if we understand the basic principles involved.
As an example consider the motion of the Earth around the Sun. The Sun and Earth attract each other. Once we know or model this gravitational force we can simulate the elliptic orbit of Earth.
Here we do not need a computer since the governing equation is simple.
But consider a slightly more complicated problem of a projectile hurled in the atmosphere. Here the friction of air comes into picture. It is a complicated function of the shape of the projectile, its orientation and velocity (last two are not known apriori).
The trajectory can be simulated by approximate numerical techniques. We start with the condition of the projectile (position and velocity; then frictional force is known) at some instant. We can calculate its condition after a very small time interval.
Then the new value for friction can be evaluated. We continue this process of numerical integration to get the trajectory. Smaller the time interval employed more accurate is the solution.
This is where the computer enters, which can do the four basic arithmetical operations at a high speed and without mistakes.
Digital computers entered the scene in the mid 20th century and have become powerful tools in simulating different physical phenomena.
The complicated equations governing a phenomenon are approximated by a large system of simultaneous equations. The role of the computer is to solve this system of equations. The methods to solve simultaneous equations are known for centuries.
But we did not know even at the beginning of the 20th century whether these methods would lead to the accurate solution if the system contains, say 40 equations.
More the number of equations better is the simulation but more is the effort required by the computer.
Today millions of equations are solved literally millions of times, thanks to the good algorithms and powerful computers.
Complex fluid flow phenomena like turbulent flows, vibration of an aeroplane frame, combustion, weather, ocean circulation, chemistry of drug design, micro-electronics, nano-technology, economic modelling, formation of cosmic structures are some of the examples that need huge computing power.
Hence we hear the words super computers, parallel computation, high performance computing, tera-flops (1,000 billion arithmetical operations per second; yes!) etc. Today there are supercomputers delivering dozens of tera-flops.
But the power we have on desktop machines today was available only with supercomputers a decade or so before.
Computer simulation leads to a large volume of information. Then we need facilities to store it and also tools to analyse and understand.
Source : The Hindu
