Course syllabus

# Tillämpad numerisk strömningsmekanik Applied Computational Fluid Mechanics

## MVKN45, 7,5 credits, A (Second Cycle)

Valid for: 2015/16
Decided by: Education Board E
Date of Decision: 2015-04-13

## General Information

Elective for: F4, F4-bem, M4-fo, M4-bem, Pi4-bem
Language of instruction: The course will be given in English

## Aim

The aim of this course is to provide basic knowledge on modern computational methods which are commonly used for laminar and turbulent flows. The most common turbulence models and their effect on the numerical solution are also discussed. Furthermore, the intention is to provide skills in the analysis and evaluation of results from numerical flow simulations. This knowledge should be sufficient to be able to chose an appropriate solution strategy and estimate the accuracy of the results for a given flow case.

## Learning outcomes

Knowledge and understanding
For a passing grade the student must

• be able to discuss the potential and limitations of computational fluid dynamics
• be able to describe different methods for numerical solution of flow problems and their applicability for different types of flow
• be able to describe the build-up of the most common RANS based turbulence models and how these can affect the numerical flow solution
• be able to describe the process from a mathematical description to numerical solution of a fluid mechanical problem, and under which conditions the system is soluble.
• be able to describe the sources of errors in the process from mathematical description to numerical solution of a fluid mechanical problem and how these errors affect the solution
• be able to explain some of the important and basic terms of the subject

Competences and skills
For a passing grade the student must

• be able to analyse a flow case and suggest a strategy for the solution of it with respect to governing equations, possible simplifications, choice of appropriate numerical method and turbulence model, and also to compare with alternative methods and models.
• be able to scrutinise and from given criteria estimate the credibility of results from numerical flow simulations

Judgement and approach
For a passing grade the student must

• be able to actively participate in discussion of problems relevant for the subject
• be able to present, both orally and in writing, a technical report containing analyses and choice of numerical solution method and turbulence model

## Contents

The course contains methods for numerical solution of fluid mechanical problems, both compressible and incompressible. The system of governing equations can be predominantly hyperbolic, parabolic or elliptic depending on the character of the flow. The most common numerical solution methods for these types of systems of partial differential equations are treated. The course also discusses different typrs of discretisation (finite differences and finite volumes) and how these affect the accuracy and stability of the solution. Different types of computational grids and how these affect the accuracy are also treated. Furthermore, methods for increasing computational efficiency (multi-grid methods) are also discussed. A discussion on the most common turbulence models based on the Reynolds averaged Navier-Stokes equations (RANS) and how these can affect the numerical solution is also included.

## Examination details

Assessment: Examination is individual as well as based on group work. The compulsory home assignments and laboratory exercises are reported in writing, individually. No report is required from the computer exercises, however attendance is compulsory. The project assignment is reported group-wise both in writing and orally at a seminar, where all group members shall participate actively. The examination also includes a test on the theoretical content of the course. To pass it is required that all compulsory parts, i.e. home works, project assignment and the test are approved. The grade is based on the home works, project assignment.

• MMV211 Fluid Mechanics or MMVF01 Thermodynamics and Fluid Mechanics
• FMA430 Calculus in Several Variables or FMA435 Calculus in Several Variables
• FMA420 Linear Algebra

The number of participants is limited to: No
The course overlaps following course/s: MVK150