Modelling and Numerical Methods

Welcome to the Modelling and Numerical Methods course.

Table of contents

• List of Symbols/Notation

• 1. Intro to Vector/Tensor Calculus
  • 1.1 Continuum Mechanics and Vector Calculus
  • 1.2 Vector Transformations
  • 1.3 Intro to Tensors
  • Exercises
• 2. Stress and Tensors
  • 2.1 Stress and Tensors
  • Exercises
• 3. Kinematics and Strain
  • 3.1 Kinematics
  • Exercises
• 4. Conservation Equations
  • 4.1 Conservation Equations
  • 4.2 Rheology
  • Exercises
• 5. Dimensional Analysis
  • 5.1 Dimensions and Dimensional Analysis
  • Worksheet

• 6. Potential Flow
  • 6.1 Potential Flow
  • Worksheet
• 7. Navier-Stokes
  • 7.1 Solving Navier-Stokes Numerically
  • Worksheet
  • Solvers
• 8. Turbulence and Non-Newtonian Flows
  • 8.1 Turbulent and Non-Newtonian Flows
  • Worksheet

• 9. Interpolation Quadrature 2
  • 9.1 Interpolation & Quadrature 2
  • Homework
• 10. ODE Solvers 2
  • 10.1 ODE solvers 2
  • Homework
• 11. PDE Solvers: Finite Difference Methods 2
  • 11.1 PDE Solvers: Finite Difference Methods 2
  • Homework
• 12. Finite Element Methods
  • 12.1 Finite Element Methods
  • Homework

Acknowledgments

Teaching Material:

• Professor Saskia Goes: Lecture Notes and Worksheets for Chapters 1-4

• Professor Stephen Neethling: Lecture Notes and Worksheets for Chapters 5-8

• Professor Matthew Piggott: Lecture Notes and Worksheets for Chapters 9-12

Jupyter Book Compilation:

• Noah Collins

• Karthik Krishnan

• Supervised by Dr Rhodri Nelson