Advanced Computation in Fluid Mechanics (DD2365), 7.5hp, Spring 2016

Advanced Computation in Fluid Mechanics

The course focuses on four topics:

• FEM for incompressible flow.
• FEM for the time-dependent Navier-Stokes equations.
• Error estimation and adaptive methods for the Navier-Stokes equations.
• Computational methods for turbulent flow.

Recommended prerequisites 

SF2561 The Finite Element Method 

Course activities

• 4 lectures/labs
• 3 project seminars

Course goals

The goal of the course is to present efficient computational methods for fluid mechanics simulations, with focus on adaptive finite element methods (FEM) for incompressible flow, and to train the student to apply these computational methods to address fluid mechanics problems. Research challenges in the field are highlighted, e.g. with respect to simulation of turbulent flow.

After completion of the course the student will be able to:

• Formulate an adaptive FEM method for the Navier-Stokes equations.
• Carry out a basic stability analysis of a FEM method for the Navier-Stokes equations.
• Carry out a basic a posteriori error analysis of a FEM method for the Navier-Stokes equations.
• Implement an adaptive FEM method for the Navier-Stokes equations in a FEM software.
• Account for the characteristics of different computational methods for turbulent flow. 

Examination 

• Project report and presentation 
• Written exam based on lectures, labs and project

Teachers

Johan Hoffman

Literature

[CTIF] J.Hoffman and C.Johnson, Computational Turbulent Incompressible Flow, Springer, 2007 (order, download)

[NMIF] Martin Burger, Numerical Methods for Incompressible Flow

Software 

FEniCS [download software to your computer] 

FEniCS-cloud [run software through your web browser]

FEniCS-HPC [run HPC version of software on PDC supercomputer Beskow]

Apply for a PDC account

Add-on studies

Contact the course leader about project work.  

Preliminary week schedule

Week 1

Introduction 

Apply for a PDC account

Week 2

FEM for incompressible flow. 

Week 3

FEM for the time-dependent Navier-Stokes equations.

Week 4

Error estimation and adaptive methods for the Navier-Stokes equations.

Week 5

Computational methods for turbulent flow.

Week 6

Project seminar 

Week 7

Project seminar 

Week 8

Project seminar: final presentation 

Week 9

Written exam.