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

First lecture: Wednesday March 30, 11.15 in room M38. 

Advanced Computation in Fluid Mechanics

The course focuses on four topics:

• FEM for steady, viscous flow: Stokes equations. 
  
• FEM for the unsteady flow: 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 goal

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 

• Lab reports, project report and project presentation 
• Written exam based on lecture notes, labs and project
• Exam preparation questions 

Labs

The labs can be done in groups of 2-3 students: 

• Lab 1: FEM for Stokes equations
• Lab 2: FEM for Navier-Stokes equations
• Lab 3: Adaptive FEM for Navier-Stokes equations [labadaptive.ipynb]

The lab reports should should be sent to the teacher by email as one pdf-file. The code written should be submitted to the teacher by email for verification, or made available as a Python notebook (Labs 1-3). 

Project

The project can be done in groups of 2-3 students, focused on one research question formulated by the group connected to the course topics. The report should consist of the following parts: 

• Background
• Research question
• Method 
• Results
• Discussion

The report should consist of max 5 pages using font Times New Roman 12pt, and should be submitted to the teacher by email as one pdf-file. The code written should be submitted to the teacher by email for verification. 

Teachers

• Johan Hoffman
• Johan Jansson
• Niyazi Cem Degirmenci

Literature

• [CFD] Adaptivity and Computability in CFD [preprint]
• [AFEM] Jansson et al., Framework for massively parallel AFEM CFD on tetrahedral meshes
• [TET] Bey, Tetrahedral Grid Refinement
• [CRS] Reuter, Coarsening of Simplicial Meshes for Large Scale Parallel FEM Computations
• [ALE] Huerta et al., Arbitrary Lagrangian–Eulerian Methods
• [MOPT] Freitag, Knupp, Tetrahedral mesh improvement via optimization
• [FSI] Hoffman et al., Unified continuum modeling of fluid-structure interaction
• [CTIF] Computational Turbulent Incompressible Flow, Springer, 2007 (order, download)
• [NMIF] Martin Burger, Numerical Methods for Incompressible Flow 
• [LFEM] Endre Süli, Lecture notes on finite element methods for partial differential equations
• [FEniCS] FEniCS book: Automated solution of differential equations by the finite element method

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.  

Extra material

• Univeristy of Michigan FEM MOOC

Preliminary week schedule

Week 1

• Lecture notes 0 
• Register for the course
• Email Cem Degirmenci <ncde@kth.se> to obtain username/password for FEniCS-cloud
• Apply for a PDC account
• Review fluid dynamics: [NMIF] chapters 1-3
• Review finite element methods: [LFEM] chapters 1-3 

Week 2

• FEM for steady, viscous flow: Stokes equations.
• Lecture notes 1
• Lab 1: FEM for Stokes equations
• Stokes equations: [NMIF] chapter 4

Week 3

• FEM for the unsteady flow: Navier-Stokes equations.
• Lecture notes 2
• Lab 2: FEM for Navier-Stokes equations
• Navier-Stokes equations: [NMIF] chapter 5-6

Week 4

• Error estimation and adaptive methods for the Navier-Stokes equations.
• Lecture notes 3
• Lab 3: Adaptive FEM for Navier-Stokes equations [labadaptive.ipynb]

Week 5

• Computational methods for turbulent flow: tutorial FEniCS-HPC
• Adaptivity and Computability in CFD [preprint]
• Lab 4: Adaptive FEM for turbulent flow

Week 6

• Project seminar: problem statement 

Week 7

• Project seminar: first results  

Week 8

• Project seminar: final presentation 

Week 9

• Written exam.