# 151-0182-00L Fundamentals of CFD Methods

Semester | Autumn Semester 2020 |

Lecturers | A. Haselbacher |

Periodicity | yearly recurring course |

Language of instruction | English |

Abstract | This course is focused on providing students with the knowledge and understanding required to develop simple computational fluid dynamics (CFD) codes to solve the incompressible Navier-Stokes equations and to critically assess the results produced by CFD codes. As part of the course, students will write their own code and verify and validate it systematically. |

Objective | 1. Students know and understand basic numerical methods used in CFD in terms of accuracy and stability. 2. Students have a basic understanding of a typical simple CFD code. 3. Students understand how to assess the numerical and physical accuracy of CFD results. |

Content | 1. Governing and model equations. Brief review of equations and properties 2. Overview of basic concepts: Overview of discretization process and its consequences 3. Overview of numerical methods: Finite-difference and finite-volume methods 4. Analysis of spatially discrete equations: Consistency, accuracy, stability, convergence of semi-discrete methods 5. Time-integration methods: LMS and RK methods, consistency, accuracy, stability, convergence 6. Analysis of fully discrete equations: Consistency, accuracy, stability, convergence of fully discrete methods 7. Solution of one-dimensional advection equation: Motivation for and consequences of upwinding, Godunov's theorem, TVD methods, DRP methods 8. Solution of two-dimensional advection equation: Dimension-by-dimension methods, dimensional splitting, multidimensional methods 9. Solution of one- and two-dimensional diffusion equations: Implicit methods, ADI methods 10. Solution of one-dimensional advection-diffusion equation: Numerical vs physical viscosity, boundary layers, non-uniform grids 11. Solution of incompressible Navier-Stokes equations: Incompressibility constraint and consequences, fractional-step and pressure-correction methods 12. Solution of incompressible Navier-Stokes equations on unstructured grids |

Lecture notes | The course is based mostly on notes developed by the instructor. |

Literature | Literature: There is no required textbook. Suggested references are: 1. H.K. Versteeg and W. Malalasekera, An Introduction to Computational Fluid Dynamics, 2nd ed., Pearson Prentice Hall, 2007 2. R.H. Pletcher, J.C. Tannehill, and D. Anderson, Computational Fluid Mechanics and Heat Transfer, 3rd ed., Taylor & Francis, 2011 |

Prerequisites / Notice | Prior knowledge of fluid dynamics, applied mathematics, basic numerical methods, and programming in Fortran and/or C++ (knowledge of MATLAB is *not* sufficient). |