Complex models and advanced methods in fluid mechanics

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

1. Flow around a cylinder

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

2. Power Law fluids

• Source code
• Exercise sheet

3. Viscoelasticity

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

Lecture Agenda:

0. Introduction

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

1. Introduction to Non-Newtonian fluids

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

2. Power-law fluids

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

3. Visco-elasticity

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

4. 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)