Course content

Classification of the basic equations for fluid mechanics and heat transfer. Discretization of transport equations for compressible and incompressible flow. Finite volume methods for heat transfer and fluid flow in one and more dimensions: Diffusion, advection, convection-diffusion, Burgers', Euler and Navier-Stokes equations. Numerical solution of conservation laws and inviscid flow with modern upwind methods. Numerical solution of the unsteady gas dynamical equations. The SIMPLE and SIMPLER algorithms for the coupling of pressure and velocity for incompressible flow. Steady state and unsteady problems. Solution of algebraic systems of equations. Basics of turbulence modeling and grid generation. Introduction to a computational fluid dynamics (CFD) tool and application to heat and fluid flow.

Learning outcome

The course gives an introduction to numerical simulation of heat transfer and fluid flow problems in industrial and natural processes. Emphasis is put on learning the practical use of numerical methods and to train their programming in Matlab and Fortran. The students will learn to assess the accuracy and to interpret the meaning of the numerical results in heat transfer and fluid flow.

Knowledge:
After completion of this course, the student will have knowledge on:
- Classification of the basic equations for fluid dynamics and heat transfer.
- Discretization of transport equations for compressible and incompressible flow.
- Finite volume methods for heat transfer and fluid flow in one and more dimensions: Diffusion, advection, convection-diffusion, Euler and Navier-Stokes equations.
- Numerical solution of inviscid flow with modern upwind methods.
- Numerical solution of the unsteady gas dynamical equations.
- The SIMPLE and SIMPLER algorithms for the coupling of pressure and velocity for incompressible flow.
- Steady state and unsteady problems.
- Solution of algebraic systems of equations.
- Basics of turbulence modeling and grid generation.
- Introduction to a computational fluid dynamics (CFD) tool and application to heat and fluid flow.

Skills:
After completion of this course, the student will have skills on:
- Practical use and programming of numerical methods in heat transfer and fluid dynamics.
- Checking and assessing the accuracy of numerical results.
- Interpretation of the numerical results in heat transfer and fluid dynamics.
- Consistency analysis, modified equation analysis and von Neumann stability analysis of finite difference methods.
- Derivation and use of characteristic boundary conditions.
- Implementation of Dirichlet and Neumann boundary conditions in finite volume methods.
- Checking and accelerating iterative methods for the solution of systems of equations.
- Use of staggered grid and SIMPLE algorithm for the incompressible Navier-Stokes equations.

General competence:
After completion of this course, the student will have general competence on:
- Numerical solution of practical problems in heat transfer and fluid dynamics.
- Checking and assessing numerical methods and simulations for heat transfer and fluid flow problems.

Learning methods and activities

Lectures and lessons. Learning is based on extensive student activity in the form of solving exercise problems. The exercises include one larger exercise where the students develop their own program for solving heat and fluid flow problems. Programming in Matlab and Fortran. The teaching will be in English when students who do not speak Norwegian take the course. If the teaching is given in English the examination papers will be given in English only. Students are free to choose Norwegian or English for written assessments.

Compulsory assignments

• Homework problems

Recommended previous knowledge

Recommended prerequisites: TEP4280 Introduction to Computational Fluid Dynamics, TEP4135 Engineering Fluid Mechanics, and TEP4130 Heat and Mass Transfer, or equivalent courses.

Course materials

Richard H. Pletcher, John C. Tannehill, Dale A. Anderson: Computational Fluid Mechanics and Heat Transfer, 3rd edition, CRC Press, Boca Raton, 2013. Lecture notes, Matlab and Fortran 90 programs.

Credit reductions