TABLE OF CONTENTS Numerical simulation using computers or computational simulation has increasingly become a very important approach for solving complex practical problems in engineering and science. Numerical simulation translates important aspects of a physical problem into a discrete form of mathematical description, recreates and solves the problem on a computer, and reveals phenomena virtually according to the requirements of the analysts. Rather than adopting the traditional theoretical practice of constructing layers of assumptions and approximations, this modern numerical approach attacks the original problems in all its detail without making too many assumptions, with the help of the increasing computer power.
Numerical simulation provides an alternative tool of scientific investigation, instead of carrying out expensive, time-consuming or even dangerous experiments in laboratories or on site. The numerical tools are often more useful than the traditional experimental methods in terms of providing insightful and complete information that cannot be directly measured or observed, or difficult to acquire via other means.
Numerical simulation with computers plays a valuable role in providing a validation for theories, offers insights to the experimental results and assists in the interpretation or even the discovery of new phenomena. It acts also as a bridge between the experimental models and the theoretical predictions as schematically shown in Figure 1.1.
