2.4.2　Mathematical simulation

The mathematical simulation method refers to the simulation that two physical phenomena or processes are completely different in physical essence but have the same mathematical forms.Mathematical simulation is also called after analogy.It satisfies neither geometric similarity nor physical similarity conditions.The original content as well as the built model have nothing in common in form or essence of physical laws,but they do follow the same mathematical forms.

For example,the electrostatic field and the steady current field are originally two different fields,but the physical laws followed by these two fields have the same mathematical forms.Therefore,the steady current field can be used to simulate the electrostatic field which is hard to measure directly.And the potential distribution in the constant current field is used to simulate the potential distribution of the electrostatic field.(https://www.daowen.com)

If the above two simulation methods are well used,they will certainly be much more effective.Simulation is a simple and easy testing method,which is widely used in modern scientific research and engineering design.For example,in the development of space science and technology,simulation experiments are usually carried out to obtain reliable and necessary experimental data.Simulation is very useful in hydropower construction,underground mineral exploration,and electric vacuum device design.

It should be pointed out that the computer simulation which uses the computer to carry out experimental aided design and simulation experiments has become a brand-new simulation method.The extensive application of computers in the natural science fields has brought great revolution for these researches on physical experiments.Computers can be used to process data in physics experiments,control the experimental process through analog-to-digital and digital-to-analog conversion,demonstrate physical phenomena and physical processes through computer simulations,conduct computer-aided experiments or corresponding aided design and many others.Computational physics,which is currently believed to be the same important as experimental physics and theoretical physics has become the third pillar of physics.Especially,some methods in the computational physics are identical with that in the computer simulation.