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What Is Numerical Simulation?
A model is a testable representation of a system. Numerical simulation consists of translating a mathematical model into numerical language in order to perform complex calculations more easily.
Discerning readers may skip to the next chapter.
1.1 What Is a Model?
A model of a system is an experienceable representation.
Let’s begin with defining what a system is. It is an object (real or abstract) or a set of objects that we are willing to study. It is a very broad concept: for instance, a system may be a plane, an engine, or even a screw. Note that it may contain subsystems that are systems as well. So, in industry, teams work on systems on a daily basis (these systems will be products or parts of products marketed by the company), either to conceive, develop, or produce them.
There are many possible representations of a single system. In this work, we will deal with a mathematical representation; that is to say, the representation aims at describing its behavior through equations. Those equations often come from known laws of physics (such as the forces of gravity or the fundamental principles of dynamics). The representation of a system may be understood as a rationalization of reality or a vision of a system through one angle.
In industry, a wide range of systems are constantly tested through live experiments. For example, we are able to test an aircraft engine to assess the temperatures its compartments can reach or to test a screw to determine what mechanical stresses it can resist. Also, a system representation can be tested. This experiment will consequently be virtual.
Let’s illustrate this concept with an example, represented by the figure below, assuming that our goal is to assess the duration of an ice cube melting in a glass of water (Figure 1.1).
FIGURE 1.1
The system studied: an ice cube floating in a glass of water.
The system studied here is an ice cube—that is to say, the volume of water initially contained in it. The rest of the water filling the glass will be the environment of the system. We will build a representation of the ice cube, making it simpler.
We consider that the ice cube exchanges, by convection, with the rest of the water contained in the glass. Using thermodynamics, we can assume that the exchanged heating power will be
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