# Complex models and advanced methods in fluid mechanics

Summer semester 2017

**Complex models and advanced methods in fluid mechanics**

Tue. 13:15 - 14:45 G02-20 and Wed. 09:15 - 10:45 G02-20

**Computational Exercises**

- Flow around a cylinder

- Problem 7 from Gascoigne Course
- Source code
- Exercise sheet

- Power Law fluids

- Viscoelasticity

- Source code
- Exercise sheet
- Solution 1st Benchmark
- Lid driven cavity paper
- Mesh generator
- Reference values

**Lecture Agenda:**

- Introduction

- Review of fluid mechanics
- Review of governing equations
- Basic thermodynamic considerations

- Introduction to Non-Newtonian fluids

- Taxonomy of Non-Newtonian models
- Examples of Non-Newtonian effects (movies)

- Power-law fluids

- Shear thickening/thinning
- Overview of analytical results
- Plug flow in Gascoigne

- Visco-elasticity

- Modelling of visco-elasticity
- Overview of analytical results
- Lid driven cavity benchmark in Gascoigne

- Compressible fluids

- Euler system
- Finite Volume Method
- Discontinuous Galerkin Method
- Euler system with congestion

**Literature:**

Gascoigne packages Lecture Notes J. Málek, K. R. Rajagopal, Mathematical issues concerning the Navier-Stokes equations and some of its generalizations, Handb. Differ. Equ., Evolutionary Equations, Volume 2 (2005), Elsevier/North Holland, Amsterdam, 371-459. J. Málek, Introduction to non-Newtonian fluid mechanics (lecture notes)