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Computational fluid dynamics for turbulent flows

General details of the subject

Face-to-face degree course

Description and contextualization of the subject

In the framework of renewable energies, the study of the effects of fluid dynamics is crucial for the efficiency and performance when designing a device for energy extraction. The course covers the fundamentals of the theory and numerical simulation of fluid flow, encompassing turbulence effects in applications such as flow around platforms and turbines, etc. The mesh generation process, including goal-oriented adaptive mesh refinement, will also be tackled, since it is an essential and time-consuming component in the design process.

The students will learn the fundamentals concepts and mathematical background of computational fluid dynamics (CFD). They will learn to set-up numerical simulations for aerodynamics applications from scratch through practical hands-on sessions. They will be able to select the suitable numerical set-up for the different flow conditions. The basic knowledge will be provided for post-processing and evaluating the results in terms of numerical reliability, aerodynamic forces and performance of a designed geometry

Teaching staff

NameInstitutionCategoryDoctorTeaching profileAreaE-mail
VEGA GONZALEZ, LUISUniversity of the Basque CountryProfesorado Catedratico De UniversidadDoctorNot bilingualMathematical
KUMAR , RAHULBasque Center for Applied MathematicsOtrosDoctor


Ability to learn the fundamental fluid dynamics equations, their derivation and physical interpretation25.0 %
Ability to tackle the solution of a practical problem in aerodynamics, by the use of suitable numerical approximation25.0 %
Ability to handle and understand the basics of the development of a computer program for solving the equations of fluid dynamics25.0 %
Ability to produce concise and clear report on the home assignments and to orally discuss it25.0 %

Study types

TypeFace-to-face hoursNon face-to-face hoursTotal hours
Applied computer-based groups121022

Training activities

NameHoursPercentage of classroom teaching
Expositive classes18.0100 %
Student's personal work10.00 %
Systematised study35.00 %
Working with it equipment12.0100 %

Assessment systems

NameMinimum weightingMaximum weighting
Drawing up reports and presentations30.0 % 50.0 %
Written examination50.0 % 70.0 %


Lesson 1 Introduction to fluid dynamics

Introduction to Computational Fluid Dynamics (CFD), proprieties of a fluid, conservation principles, derivation of equations of fluid dynamics, discretization techniques: finite differences, finite volume, finite element

Lesson 2 Meshing techniques

Structured meshes, unstructured meshes, mesh adaptivity

Lesson 3 General Galerkin (G2) finite element method

Concept of weak solution, energy estimates for the underlying equations and G2 approximations, a posteriori output error estimates for G2 using duality, analysis of the global effect of friction boundary conditions in G2 computations

Lesson 4 Training in FeniCS framework

Use G2 software for adaptive turbulent flow computations with error control


Basic bibliography

1. Textbook: Blazek, J., Computational Fluid Dynamics: Principles and Applications, 3rd Edition,

Butterworth-Heinemann, 2015.

2. Acheson, D. J., Elementary Fluid Dynamics, Oxford Applied Mathematics and Computing Science Series, Oxford University Press, 1990.

3. J. Hoffman and C. Johnson "Computational Turbulent Incompressible Flow", Springer, 2007.

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