# Computational Fluid Dynamics, 7,5 HP - Kurskod kommer senare

COURSE SYLLABUS, third-cycle courses

Entry requirements:
Advanced fluid dynamics (partial differential equation formulation, Navier-Stokes, boundary layers etc) and Heat & Mass Transfer corresponding to a MSc degree in Mechanical Engineering or equivalent

Course content:
Seminar 1:

• Introduction to the course

• Lecture with an overview of CFD

• Home assignment 1: Read Chapter 1 & 2. Use your own words and explain the concepts of consistency, stability, convergence, conservation, boundedness, realizability and accuracy.

Seminar 2: Finite Difference Methods

• Discussion about Home assignment 1.

• One of the students will present an overview of Chapter 3 Finite difference methods. All other students are expected to have read the material so they can participate in the discussion about things that were difficult to understand or that are particularly important.

• Home assignment 2: Solve the example in section 3.10 but change the scheme to Linear Upwind Scheme. Compare with the results in section 3.10 and discuss advantages and disadvantages. Extra: Use the QUICK Scheme and solve the same problem. What can be said about the accuracy of this scheme when it is used in a finite volume method?

Seminar 3: Finite Volume Methods

• Discussion about Home assignment 2.

• One of the students will present an overview of Chapter 4 Finite Volume Methods. All other students are expected to have read the material so they can participate in the discussion about things that were difficult to understand or that are particularly important.

• Home assignment 3: Solve the example in Section 4.7.3 using several schemes, including the MUSCL scheme (use eq. 4.37 for the cell face variable so you can use the formulas in Table 4.2 for different schemes). Compare the MUSCL scheme results with the results in the example and discuss pros and cons. Use the other results and compare to the results in the book to check that you have programmed the problem correctly. Is the MUSCL scheme TVD?

Seminar 4: Solution of linear equation systems

• Discussion about Home assignment 3.

• One of the students will present an overview of Chapter 5 Solution of linear equation systems. All other students are expected to have read the material so they can participate in the discussion about things that were difficult to understand or that are particularly important.

• Home assignment 4: Use the discretization from the previous home assignment to assemble the system matrix. Select several different iterative methods, including one that has not been used in the example in section 5.8, and solve the problem. Use the error estimate in section 5.7 to assess the performance of the methods. Plot the results in the same way as in the example and discuss your results. Notice that the error estimate can be used for non-linear systems when the solution is close to the converged result. Discuss the behavior of the residuals. Is the largest eigenvalue of the iteration matrix real or complex? Take a residual plot from a commercial CFD program (you can use an own result or the result from a tutorial) and analyse the behavior of the residuals in the same way, assuming that the theory is valid for non-linear systems. Use the information in the book and discuss whether the estimate from linear theory is valid or not in your case.

Seminar 5: Methods for unsteady problems

• Discussion of Home assignment 4.

• One of the students will present an overview of Chapter 6 Methods for unsteady problems. All other students are expected to have read the material so they can participate in the discussion about things that were difficult to understand or that are particularly important.

• Home assignment 5: Solve the two examples in section 6.4 using a third or fourth order Runge-Kutta method. Compare the results with those in the book.

Seminar 6: Solution of the Navier-Stokes equations

• Discussion of Home assignment 5.

• Two of the students will present an overview of Chapter 7 & 8 Solution of the Navier-Stokes equations; Part 1 & 2. All other students are expected to have read the material so they can participate in the discussion about things that were difficult to understand or that are particularly important.

• Home assignment 6: Will be defined later. The problem will be solved using one of the codes available at the book’s download site.

Seminar 7: Complex geometries

• Discussion of Home assignment 6.

• One of the students will present an overview of Chapter 9 Complex geometries. All other students are expected to have read the material so they can participate in the discussion about things that were difficult to understand or that are particularly important.

• Home assignment 7: Will be defined later. The problem will involve complex geometry and be solved with a commercial code (e.g. Star CCM+ or Ansys CFX) .

Seminar 8: Efficiency and accuracy improvement

• Discussion of Home assignment 7.

• One of the students will present an overview of Chapter 12 Efficiency and accuracy improvement. All other students are expected to have read the material so they can participate in the discussion about things that were difficult to understand or that are particularly important.

• Home assignment 8: Final home assignment will be defined together with each student. The task will be to solve a problem that is connected to the students own research. The numerical details in and the results from the computational model shall be described and discussed in light of the lessons learned from the course.

Learning outcomes:

After the course the participants shall be able to:

• Describe in detail how a finite volume CFD method is formulated, discretized and programmed and understand the strengths and weaknesses of the different options that are available

• Make an educated choice of numerical solution methods (linear solvers, time integration, resolution of non-linearities, etc.) and sub models for the problem in question

• Understand how different types of boundary conditions are implemented and what the requirements on the solution are for the boundary conditions to be valid.

• Assess the convergence during the solution of complex flow problems

• Estimate the accuracy of the solution to a complex flow problem and use the result to choose an optimum size grid that makes it possible to perform multiple simulations with reasonable accuracy and within a reasonable calender time.

• Understand the reason for poor convergence or divergence and choose a remedying solution to that problem.

Course methods:

The course consists of an introductory lecture and a series of seminars during which the content of the course literature is discussed. The seminars will also include a discussion of the home assignments that are given for each major section of the course. Before each seminar one or more of the students will prepare a summary of the material that will be presented during the seminar. All students are expected to be well prepared and to actively participate in the discussion of the material.

A number of home assignments will be given. All home assignments except the last will be corrected by the students themselves to stimulate discussion among the students. The last home assignment will be corrected by the course leader. Each home assignment will be discussed with the whole group and the course leader in the following seminar. Each home assignment shall be reported as a short technical report. The report should include a proposal for improved definition of the problem that can be used in the next round of the course.

Examination form:

Course examination is based on the replies to the home assignments and active participation in the seminars.

Course literature:

Joel H Ferziger, Milovan Peric, Robert L Street, Computational Methods for Fluid Dynamics, 4th edition, Springer, 2019

Extra: Patankar SV, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing, 1980

Best Practice Guidelines for CFD, ERCOFTAC, 2000

Education cycle: From November 2019 to February 2020

Course is given periodically: Approximately bi-annually

Send application to: Professor Rikard Gebart; rikard.gebart@ltu.se
Doctoral student enter name, civic registration number, e-mail, Division and Department in the application

190925

Course open for application by doctoral students admitted to other universities than LTU: Yes, if they are exchange students and are present at LTU during the seminars (no video link)

Limited number of students: Approximately ten students.

Tuition:
If the course is allocated resources via internal resource allocation system, the course is free of charge for doctoral students admitted at LTU, for doctoral students admitted to other universities, course fees may be required. For other courses the Department decides on course fees.

Contact person:

Rikard Gebart, rikard.gebart@ltu.se, 2196

Examiner:
Professor Rikard Gebart

Course syllabus decided by:

Date of decision:

## Kontakt

### Rikard Gebart, Professor

Telefon: 0920-492196
Organisation: Energiteknik, Energivetenskap, Institutionen för teknikvetenskap och matematik