NUMERICAL METHODS: MATHEMATICAL MODEL

MATHEMATICAL MODEL
Can be defined generally as a formulation or equation expressing the fundamental characteristics of a system or physical process in mathematical terms. The models are classified from simple algebraic relationships to large, complicated systems of differential equations.

Mathematical modeling, besides being an activity that fits into applications of mathematics and provides a link between these and other scientific and technical areas within the scope of the investigation, has also emerged as a powerful educational tool.

Imagen tomada: dcb.fi-c.unam.mx/users/gustavorb/MN.html

The implementation of a mathematical model is the way it uses science and technology to approach reality and solve problems. As a result, mathematical objects are necessary to understand the technological and scientific concepts through constructions and results. Mathematical models provide a framework in which are interrelated concepts of different sciences and in this sense, modeling appears as an important tool to teach math and science. Moreover, the use of models can help reinforce basic science concepts, enriching the learning. (1)

START MAKING YOUR PARTY:
Identification of variables causing the change in the system
Establishment of reasonable assumptions about a model system for mental, verbal and graphic

CHARACTERISTICS OF A MODEL
1. Describes a natural process or system
2. Represents a simplification and an idealization of reality
3. Leads to reproducible results

SIMULATED ENVIRONMENTS
What is really a numerical method of simulation?
Is trying to represent a physical phenomenon based on a small portion of the total being analyzed.
Its purpose is to simulate actual conditions scale, today facilmento is achieved with computer graphics.
The following video shows how automated are the oil rigs. Computer Graphing

DARCY'S LAW
Darcy's Law describes, based on laboratory experiments the characteristics of the flow of fluid through a porous medium.

The simplest formulation of the law (for linear systems) can be considered almost "intuitive": The flow of a fluid flowing through a porous medium depends linearly:

The geometrical properties of the system: Area (A) and length (L).
The fluid characteristics: Mainly its viscosity (μ).
The flow conditions: Differential Pressure (DP) between the edges of the system.

This makes it almost "obvious" that, equality of the other system variables, the flow rate (Q) flowing through a porous medium grows directly with the applied pressure difference and the available flow area and decreases when increases the length and fluid viscosity.

Analytically this dependence is expressed by the following formula: