Explore UCD

UCD Home >

ACM40890

Academic Year 2024/2025

Advanced Fluid Mechanics (ACM40890)

Subject:
Applied & Computational Maths
College:
Science
School:
Mathematics & Statistics
Level:
4 (Masters)
Credits:
5
Module Coordinator:
Assoc Professor Lennon Ó Náraigh
Trimester:
Spring
Mode of Delivery:
On Campus
Internship Module:
No
How will I be graded?
Letter grades

Curricular information is subject to change.

This module introduces advanced concepts and methods in Fluid Dynamics.
The main focus is on viscous incompressible flows, under the following
broad headings.

[Canonical examples of fluid instability:] Eigenvalue analysis of linear
instability in the Rayleigh-Benard, Rayleigh-Taylor, and Kelvin-Helmholtz
systems. Eigenvalue analysis of parallel flow instability leading to the
Orr--Sommerfeld equation.

[Parallel flow instability beyond the temporal theory:] Absolute and
convective instability, transient growth.

[Weakly nonlinear stability theory:] Stuart--Landau theory applied to the
Cahn-Hilliard and Kuramoto--Sivishinsky equation.

[Problems in turbulence:] Kolmogorov spectra. Wall-bounded turbulence and
Reynolds averaging. Closure models. Discussion of direct numerical
simulation and large-eddy simulation. The notion of wall-functions in
large-eddy simulation.

[Introduction to High-Performance computing:] Solving sparse linear
problems iteratively. Applications of such methods to Computational Fluid
Dynamics. Introduction to multithread and multicore programming in
Fortran.

About this Module

Learning Outcomes:

On completion of this module students should be able to
1. Write down the eigenvalue problem for the canonical physical systems of
Fluid Dynamics
2. Derive the Orr--Sommerfeld equation and compute exact solutions in
certain cases
3. Describe the subtle features of linear stability theory beyond temporal
eigenvalue analysis
4. Carry out a Stuart--Landau analysis on simple nonlinear equations
5. Characterize turbulence using the Kolmogorov and Reynolds-averaged
theories.
6. Solve sparse linear problems iteratively and implement their solution
in a programming language of the student's choice.

In addition to the study of sparse linear systems and their role in
Computational Fluid Dynamics, a number of mini-projects will form part of
this module. Therefore, on completion of this module students should gain
much familiarity with computational methods in fluids. In particular,
students should further be able to

1. Perform an Orr--Sommerfeld stability analysis of Poiseuille flow using
spectral methods in Matlab
2. Solve nonlinear wave equations numerically to test for the
applicability of Stuart--Landau theory
3. Implement an existing parallel flow solver (S-TPLS) to study large-eddy
simulations in turbulent channel flow
4. Analyse the turbulent statistics emanating from the simulations under
item (3) above.

Student Effort Hours:
Student Effort Type Hours
Lectures

24

Specified Learning Activities

26

Autonomous Student Learning

50

Total

100


Approaches to Teaching and Learning:
Lectures and problem-based learning

Requirements, Exclusions and Recommendations
Learning Recommendations:

MSc / PhD level module. Students are therefore expected to have completed prior modules in Complex Analysis and Partial Differential Equations, at least two prior modules in Fluid Dynamics, and at least one prior module in Computational Science with significant programming content


Module Requisites and Incompatibles
Not applicable to this module.
 

Assessment Strategy
Description Timing Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Exam (In-person): Class test - one hour Week 9 Standard conversion grade scale 40% No
50
No
Group Work Assignment: Group Project Week 12 Standard conversion grade scale 40% No
50
No

Carry forward of passed components
No
 

Resit In Terminal Exam
Autumn Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 

Feedback Strategy/Strategies

• Feedback individually to students, on an activity or draft prior to summative assessment

How will my Feedback be Delivered?

Not yet recorded.

Name Role
Professor Frederic Dias Lecturer / Co-Lecturer

Timetabling information is displayed only for guidance purposes, relates to the current Academic Year only and is subject to change.
Spring Lecture Offering 1 Week(s) - 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33 Wed 13:00 - 14:50