Abstract:

In an attempt to provide knowledge in Computational Fluid Dynamics (CFD) for undergraduate students of engineering schools a large amount of didactic material is being developed by different Universities throughout the word. However, this topic remains challenging for both teachers and students due mainly to the lack of previous knowledge about numerical analysis on the part of the student, the use of teaching materials focused for experts on the part of the professors, and the lack of time to develop codes by the student due to a limitation on the number of hours in the subject of CFD.

Following this approach, the student is limited to learn and understand from a mathematical point of view, algorithms and procedures, which are based on physical reasons and that are difficult to understand. This learning process is discouraging for the students, since they do not see the relation between the strong backgrounds in mathematics required to pass the subject and its real applicability.

One of the most popular numerical schemes at the end of the last century was the proposed by [1], JST model. This scheme established the foundations of the modern CFD, showing to the engineering company that is feasible simulate flows on real engineering problems. Although today this scheme is outdated, the physical approach followed by the authors do this method very interesting from a pedagogical point of view. The fact that this method has been replaced by new approaches, justifies why the only information available about it can be found basically in research articles from the end of the last century or in specialized books (see [2]), all of them beyond the capabilities and background of the students.

This paper aims to identify some of the challenges in teaching Computational Fluid Dynamics for undergraduate students, tries to identify the shortcomings of classical approaches to the teaching of this topic and makes a proposal based on the JST model and focused on the physics of the problem to solve. The main goal of this work is to provide useful material for the teacher and also to propose an alternative to increase the student interest in this subject.

The curriculum of this activity is planed for five sessions of 2 hours each, and will be detailed at the time of the conference:
Lecture 1: Introduction of the problem. Navier-Stokes equation
Lecture 2: Methodology. Stability of a numerical scheme
Lecture 3 and 4: Solving Navier-Stokes equations, and studding the numerical scheme
Lecture 5: Analyzing the results obtained and extracting some conclusions.

It is remarkable that the idea of this tutorial is to be used in advanced level courses of the degree in engineering or even in master level. Thus, to follow this activity, the student must have basic knowledge of calculus, fluid mechanics and computation.

References:
[1] A. Jameson, W. Schmidt and E. Turkel, “Numerical Solution of the Euler Equations by Finite Volume Method using Runge-Kutta Time Stepping Schemes”, AIAA Paper 81-1259
[2] J. Blazek “Computational Fluid Dynamics. Principles and Applications”, Elsevier Ltd, Third Eddition, 2005

Keywords:

Computational Fluid Dynamics, JST scheme, Euler Equations, Spatial and Temporal integration, Stability analysis and Python.