Course content

Solution strategy of CFD: from fluid flow problem to post-processing of its numerical solution, Sources of error, Examples of CFD applications. Basics of partial differential equations (PDEs) in fluid dynamics, Initial value problems: hyperbolic and parabolic PDEs, Boundary value problems: elliptic PDEs, Boundary conditions, Well-posed problems. Spatial discretization methods: Finite difference method, consistency, stability, convergence, Finite volume method, Weighted residual ansatz, idea of finite element and spectral methods. Time discretization methods: Explicit and implicit methods, Linear multistep methods, Runge-Kutta methods, Stability analysis. Numerical solution of advection and wave problems: Central and upwind methods, CFL condition. Numerical solution of diffusion problems: Explicit and implicit methods, von Neumann stability analysis. Numerical solution of stationary problems: Direct and iterative methods, Tridiagonal matrix algorithm (TDMA). Numerical solution of conservation laws:
Burgers’ equation, Navier-Stokes equations.

Learning outcome

Learning outcome:
The course provides an introduction to computational fluid dynamics. The students will train the numerical solution of model problems by developing and testing own MATLAB programs. The students will learn to assess the quality of numerical results and the efficiency of numerical methods for basic fluid flow problems.
Knowledge: After completion of this course, the student will have knowledge on: - Classification of the basic equations of fluid dynamics. - Basic space and time discretization methods. - Numerical solution of advection, diffusion and stationary problems. - Numerical solution of conservation laws. - Analysis of accuracy and stability of finite difference methods for model equations.
Skills: After completion of this course, the student will have skills on: - Practical use and programming of numerical methods in fluid dynamics. - Checking and assessing the accuracy of numerical results. - Assessing the efficiency of numerical methods. - Consistency analysis and von Neumann stability analysis of finite difference methods. - Choosing appropriate boundary conditions for model problems.
General competence: After completion of this course, the student will have general competence on: - Numerical solution of model problems in fluid dynamics. - Checking and assessing basic numerical methods for fluid flow problems.

Learning methods and activities

Lectures and lessons. Learning is based on extensive student activity in the form of solving exercise problems. Programming in Matlab. One tutorial with a CFD tool, e.g. OpenFOAM. The teaching will be in English when students who do not speak Norwegian take the course. If there is a re-sit examination, the examination form may be changed from written to oral.

Compulsory assignments

• Exercises

Recommended previous knowledge

TDT4105 Information Technology, Introduction, TEP4100 Fluid Mechanics, TMA4122 Calculus 4M, or equivalent courses.

Course materials

John C. Tannehill, Dale A. Anderson, Richard H. Pletcher: Computational Fluid Mechanics and Heat Transfer, 2nd edition, Taylor & Francis, Philadelphia, 1997.
Lecture notes, MATLAB templates.