Then, as in the figure, numerical simulation of the full problem is required to describe the system.

Thus, numerical simulations seem to be the only way to yield results of some interest.

It is mainly used in the field of direct numerical simulations.

The next figure shows the results of numerical simulations.

This landmark paper showed the first numerical simulations of a liquid.

It helps scientific applications such as numerical simulations to use more power.

Practical trials can be used to validate the result of numerical simulation.

The problem of function optimization is a very important research topic in numerical simulation.

"We're used to doing numerical simulations, so we thought, Why don't we play with this model?"

However, any numerical simulation also has an error margin.