Abstract:

The main goal of this work is to present a short guide to be used for undergraduate students of aerospace or mechanical engineering. This guide will teach the students how to link some of the main tasks learned in the first course of mathematic with computational fluid dynamics (CFD), a tool often required in industry.

The motivation of studying mathematics for students of engineering is usually low. The reason is that they believe that the content presented in this subject is difficult to understand. In addition, they need a long time (a couple of years) since they study this subject in the first course of the Engineering Degree, to see the potential and usefulness when applied to the field of engineering. Books of mathematics for engineering do not explain the different applications that can be derived from some of the formulae detailed in the manuals. If students could relate the mathematics studied in the first courses with more applied upcoming courses, their motivation would increase. It is well known that increasing student motivation will enhance their interest in the subject and the possibility of retaining the course content more easily and permanently [1].

In this article, we present relations between topics explained in infinitesimal calculus and linear algebra, and how they relate to advanced topics such as CFD. The multiple applications of CFD in the field of engineering will make the basics courses more attractive to first-degree students of engineering. In particular, we will simulate the landing gear of an airplane and will use some mathematical techniques to understand the effects (frequencies and instabilities) generated in this region of the airplane. We will emphasize the importance of studying in detail this area and explain the methods and tools used.

It is not necessary to have a strong mathematical background to understand this complex engineering application. But, the main idea of this tutorial is to give the students a general idea of how important is what they are learning, and how important is to retain the main concepts taught in the course of mathematics.

The curriculum of this activity will include the following sections that will be developed in detail at the time of the conference:
- Introduction of the general problem: the airplane and the landing gear
- The need of analyzing this region of the airplane
- Mathematics and analysis of the problem:
- Flow frequencies and instabilities
- Complex numbers
- Series
- Eigenvectors and eigenvalues
- Large computations and necessity for high performance computing in clusters
- Importance of efficient programming
- Analysis of the results obtained
We will provide a Matlab code for the students, to apply the concepts studied.

Acknowledgements:
Support from the “Subdirección de Investigación y Doctorado” of the School of Aeronautics of the Technical University of Madrid is gratefully acknowledged.

References:
[1] N.D. Daw, “The coginitive neuroscience of motivation and learning”, Social Coginition. Vol. 26, No. 5, 2008, pp. 593-620.

Keywords:

Mathematics for Engineering, Computational Fluid Dynamics, Engineering Degree, Airplane Simulations.