APP MTH 7048 - Applied Mathematics Topic A

North Terrace Campus - Semester 1 - 2017

Please contact the School of Mathematical Sciences for further details, or view course information on the School of Mathematical Sciences web site at

  • General Course Information
    Course Details
    Course Code APP MTH 7048
    Course Applied Mathematics Topic A
    Coordinating Unit Mathematical Sciences
    Term Semester 1
    Level Postgraduate Coursework
    Location/s North Terrace Campus
    Units 3
    Available for Study Abroad and Exchange Y
    Assessment ongoing assessment 30%, exam 70%
    Course Staff

    Course Coordinator: Dr Trent Mattner

    Course Timetable

    The full timetable of all activities for this course can be accessed from Course Planner.

  • Learning Outcomes
    Course Learning Outcomes
    In 2016, the topic of this course will be Modelling and Simulation of Turbulent Flows.


    Turbulent fluid flows are important in many problems of technological and scientific interest, including vehicle drag reduction, energy
    production and climate prediction, to name a few. The dynamics of  turbulence are governed by the Navier-Stokes equations,
    which are a system of nonlinear partial differential equations, for which no general solution has yet been found. Approximate solutions of
    the Navier-Stokes equations can be found numerically, but turbulent flows exhibit such a huge range of spatial and temporal
    scales that such computations are often infeasible, even on the biggest supercomputers. Consequently, simplified mathematical models that  account for the effects of turbulence are necessary in order to obtain predictions of turbulent flows. This course will
    cover the mathematical description of turbulent flows, the numerical  methods needed to solve the Navier-Stokes equations, and some of the  models used to predict turbulent flows. Topics include: Navier-Stokes equations, boundary layers, flow stability, spectral
    and finite difference solutions of the Navier-Stokes equations, mathematical description of turbulence, Reynolds-Averaged Navier-Stokes Simulations (RANS), Large-Eddy Simulations (LES), and the  stretched-vortex model. The course will have significant computational content.

    Assumed knowledge includes Fluid Mechanics III, Modelling with ODEs III and PDEs and Waves III.

    Learning Outcomes
    1 Derive and interpret the conservation equations that govern turbulent fluid flow
    2 Find and interpret similarity solutions of the Navier-Stokes equations
    3 Derive and solve boundary-layer equations for fluid flows
    4 Formulate and solve elementary flow stability problems
    5 Solve the Navier-Stokes equations numerically
    6 Use and understand common turbulent flow statistics
    7 Derive and interpret the Reynolds-averaged Navier-Stokes (RANS) equations
    8 Find similarity solutions of the RANS equations using simple turbulence models
    9 Derive and interpret the governing equations used for large-eddy simulations (LES)
    10 Understand how to apply subgrid models to run large-eddy simulations of turbulence
    University Graduate Attributes

    This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:

    University Graduate Attribute Course Learning Outcome(s)
    Deep discipline knowledge
    • informed and infused by cutting edge research, scaffolded throughout their program of studies
    • acquired from personal interaction with research active educators, from year 1
    • accredited or validated against national or international standards (for relevant programs)
    Critical thinking and problem solving
    • steeped in research methods and rigor
    • based on empirical evidence and the scientific approach to knowledge development
    • demonstrated through appropriate and relevant assessment
  • Learning Resources
    Required Resources
    Recommended Resources
    Pope, S. B., Turbulent Flows. Cambridge University Press, 2009.
    Online Learning
    This course uses MyUni exclusively for providing electronic resources, such as assignments and handouts, and for making course announcements. It is recommended that students make appropriate use of these resources. Link to MyUni login page:
  • Learning & Teaching Activities
    Learning & Teaching Modes
    This course relies on lectures as the primary delivery mechanism for the material. Tutorials supplement the lectures by providing exercises and example problems to enhance the understanding obtained through lectures. A sequence of written assignments provides assessment opportunities for students to gauge their progress and understanding.

    The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

    Activity Quantity Workload hours
    Lectures 32 96
    Assignments 4 60
    Total 156
    Learning Activities Summary
    Lecture Outline
    Week 1 Governing equations
    Week 2 Dimensional analysis and similarity
    Week 3 Boundary layers
    Week 4 Flow stabilty
    Week 5 Chebyshev spectral methods
    Week 6 Fourier spectral methods
    Week 7 Mathematical description of turbulence
    Week 8 Reynolds-averaged Navier-Stokes (RANS) equations
    Week 9 Homogeneous turbulence
    Week 10 Energy spectrum
    Week 11 RANS simulations
    Week 12 Large-eddy simulations (LES)
    Specific Course Requirements
  • Assessment

    The University's policy on Assessment for Coursework Programs is based on the following four principles:

    1. Assessment must encourage and reinforce learning.
    2. Assessment must enable robust and fair judgements about student performance.
    3. Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
    4. Assessment must maintain academic standards.

    Assessment Summary
    Assessment Task Task Type Due Weighting Learning Outcome
    Assignments Summative

    Weeks 4, 7, 10, 13

    30% all
    Exam Summative Examination period 70% all
    Assessment Related Requirements
    An aggregate score of at least 50% is required to pass the course.
    Assessment Detail
    Assessment task Set Due Weighting
    Assignment 1 Week 1 Week 4 7.5%
    Assignment 2 Week 4 Week 7 7.5%
    Assignment 3 Week 7 Week 10 7.5%
    Assignment 4 Week 10 Week 13 7.5%
    Assignments will have a maximum two week turn-around time for feedback to students.
    Course Grading

    Grades for your performance in this course will be awarded in accordance with the following scheme:

    M10 (Coursework Mark Scheme)
    Grade Mark Description
    FNS   Fail No Submission
    F 1-49 Fail
    P 50-64 Pass
    C 65-74 Credit
    D 75-84 Distinction
    HD 85-100 High Distinction
    CN   Continuing
    NFE   No Formal Examination
    RP   Result Pending

    Further details of the grades/results can be obtained from Examinations.

    Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.

    Final results for this course will be made available through Access Adelaide.

  • Student Feedback

    The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.

    SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy ( course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.

  • Student Support
  • Policies & Guidelines
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