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## Numerical simulation

Since numerical simulation needs vast computer resources(big numerical simulation programs require supercomputers and a large amount of computer resources), it is more expensive than theoretical study. But it is still much cheaper than those spacecraft used in observation. The rapid development of computer industry is also providing more and more powerful computing ability for numerical simulation, which also makes numerical simulation more applicable to a wider fields and more complex problems(Observation and theoretical study also benefit a lot from the quick development of computer technology, but their benefits from computer techniques are not so direct as that of numerical simulation). Unlike observation which has time and space limitations, as long as there is enough observation basis, numerical techniques can simulate a very large scale region and last an almost unlimited long period of time. Unlike theoretical study which can not treat complex problems, numerical simulation can deal with many physical processes at the same time. Even nonlinear processes pose no difficulty to numerical simulation.

A new important role for numerical simulation is the global extrapolation of our observations from a region, in which we do have measurements. If we run a numerical simulation and that simulation accurately predicts the observed values of parameters in the regions where we know the values, then we gain confidence in the simulation outside this region and gain global understanding. If we go further than this to incorporate observed values in a numerical simulation as it is running to keep the simulation tied to reality, we can produce an even more reliable simulation. This process is called assimilation. With the development of observation and numerical simulation, assimilation has become a new powerful method for the study of space sciences. Generally, based on observation and theoretical study, numerical simulation can help us to construct a complete understanding of the whole physical process in space. From simulation, we can also find new phenomena and processes that we still have not found in observation or theoretical study.

The development of numerical simulations began after the computer technology, so it is a fairly young method in scientific study. The quick development in this field has overcome many difficulties and made it a fairly complete system But the natural limitations of numerical simulation still exist. Just as with theoretical studies, numerical simulation results need to be confirmed by observations. Numerical simulation depends much on such components as the computation scheme and the boundary condition, etc. Sometimes, imperfect settings of the simulation process may cause the deviation of simulation result from reality. At the same time, though numerical simulations can deal with much more complex problems than theoretical study, it still can not include all the physical processes that may exist in a region. In fact, there are also many approximations made in numerical simulations, this also leads to errors in simulation results. In some cases, we need to use observational data as simulation input. Thus possible imperfect observational data can also affect the correctness of the simulation results.

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