Course Syllabus

The course will provide students with an introduction to the concepts and principles of the LES technique for numerical simulation of turbulent flows. The course will start by discussing filtering and the turbulence closure problem in the context of LES. It will then move on to derive and examine the filtered forms of the governing equations. Modeling the effect of unresolved turbulence, with Subgrid-Scale (SGS) models, will constitute a significant portion of the course content. Students will learn how to formulate SGS models, how to test SGS models off-line with experimental data and evaluate the performance of SGS models from the results of turbulent flow simulations. The last part of the class will examine issues pertaining to LES of specific flow cases of interest to the class. This will include wall-boundary conditions for wall bounded flows, SGS models for high-Reynolds number flows and SGS modeling for turbulent reacting flows. Time permitting, other topics specific to student interests will be covered.

At the end of this course, students will:

• Become familiar with the filtering concept in a turbulent flow and how the idea of scale separation forms the basis for LES.
• Gain familiarity with the filtered forms of the conservation equations (e.g., mass, momentum, turbulent kinetic energy), how they are derived and how the different terms in the equations can be interpreted.
• Obtain a basic working knowledge of common subgrid-scale (SGS) parameterizations used in LES of turbulent flows.
• Understand how to carry out a priori analysis of SGS models from experimental and Direct Numerical Simulation (DNS) data sets.
• Understand common techniques for a posteriori evaluation of SGS models and what conditions are necessary and sufficient for a 'good' SGS model.
• Become familiar with LES SGS models and techniques used in specific flow cases of interest (e.g., isotropic turbulence, high-Reynolds number boundary layers,  turbulent reacting flows, etc.)

Materials required for this course are:

• none

Recommended Texts include:

Note that you are not required to purchase any of these.  The lecture notes will encompass everything covered in the notes and handouts (journal articles book chapters) will be given as appropriate during the semester.  These books are recommended because they are the primary source used by the instructor to create a large percentage of the class material.

Please review the communication methods and requirements for this course:

Preferred Contact Methods

One way to contact me is directly using the    Inbox, located in the far left Canvas menu.

You can also contact me in the following ways:

• email: rstoll@eng.utah.edu

Office Hours

I will hold in person office hours in my office in MEK 2346 according to the following schedule (tentative):

Day(s): Friday or by appointment

Time(s): 11am-noon or by appointment

Virtual Meeting Rooms(s)

Office hours conducted through Zoom will be available depending on student preference and availability.  These will be scheduled as needed by appointment.

Grades will be based on a series of homework assignments and two course projects.  The grades in each of these categories will be broken down as follows:

Approximately 3-4 homework assignments will be given during the semester. These assignments will focus on basic topics and ideas that will be needed in the projects (statistics of turbulence, filtering, power spectra estimation, model formulations, etc.).  The assignments will be given throughout the semester when material is covered with an emphasis on the time period before the 1^st project.

Project #1:
Project #1 will focus on the application of LES SGS models in 1D turbulence simulations.  Students will be provided a basic 1D numerical code (Matlab and Python versions are available) which they will add their own SGS models to and will then examine the effect of base model type, model coefficient specification and grid resolution on the resolved simulated velocity fields.  The project will be submitted in the form of a short report (~4 pages) outlining the basics of the simulation code used, the chosen SGS models, and the parameter study results.

Project #2:
Project #2 will consist of gaining experience on doing a priori analysis of LES SGS models from experimental or numerical data.  Data sets from various experimental setups (high speed turbulence sensors, PIV) or high resolution DNS will be provided for students to use in the projects based on the students research interests.  Alternatively, if students have appropriate data sets (experimental or numerical) that they wish to use for their project they will be free to do so. The project will be submitted in the form of a short report  (~4-6 pages) including: basics and background of the SGS models to be tested, a short description of the data set used in the analysis, and a short summary of key results from the tests.  In addition to the project report, all students will be required to give a short presentation (~15 minutes) during the class's official final exam testing period (April 25, 2025 1-3pm MST).  

All assignments and projects, unless otherwise announced, must be submitted to the designated area of Canvas. Do not submit assignments via email.

Please contact the instructor prior to homework/project deadlines for accommodations.

Grading for this course

Grading in this class will follow a standard scale (see below) with the class curved as is appropriate.  Typical grades in this class are in the A to A- range for all students who complete the assigned homework and projects.  There are no exams in this class.

University of Utah grading scale

The course will cover the following

• Intro and motivation
• Analysis tools
• Turbulence and scale separation
• Equations of motion
• Filtering
• Filtered equations of motion
• Approaches to turbulence modeling
• Numerics and LES
• Basic SGS models
• eddy viscosity
• similarity
• nonlinear
• mixed
• dynamic models
• Using Fourier methods to simulate 1D turbulence (Project #1)
• Evaluating LES (a postiori)
• Evaluating SGS models (a priori, Project #2)
• Special Topics in LES (cover some set of the following examples)
• Boundary and initial conditions
• Anisotropic models
• Probability based methods
• Lagrangian particle models
• LES of compressible and/or reacting flows
• LES case studies of interest based on student input

Disclaimer

Accommodations will be considered on an individual basis and may require documentation.

Please contact your instructor and/or teaching assistant as soon as possible (preferably shortly before the semester begins) to request accommodations of any kind.

Extreme personal circumstances

Please contact your instructor as soon as possible if an extreme personal circumstance (hospitalization, death of a close relative, natural disaster, etc.) is interfering with your ability to complete your work.

Religious Practice

To request an accommodation for religious practices, contact your instructor at the beginning of the semester.

Active Duty Military

If you are student on active duty with the military and experience issues that prevent you from participating in the course because of deployment or service responsibilities, contact your instructor as soon as possible to discuss appropriate accommodations.

Disability Access

All written information in this course can be made available in an alternative format with prior notification to the Center for Disability Services (CDS). CDS will work with you and the instructor to make arrangements for accommodations. Prior notice is appreciated. To read the full accommodations policy for the University of Utah, please see Section Q of the Instruction & Evaluation regulations Links to an external site..

If you will need accommodations in this class, contact:

Center for Disability Services
  801-581-5020
  disability.utah.edu Links to an external site.
  162 Union Building
    200 S. Central Campus Dr.
     Salt Lake City, UT 84112

This syllabus is not a contract. It is meant to serve as an outline and guide for your course. Please note that your instructor may modify it to accommodate the needs of your class.

You will be notified of any changes to the Syllabus.