APP MTH 4046 - Applied Mathematics Topic A - Honours
North Terrace Campus - Semester 1 - 2016
General Course Information
Course Code APP MTH 4046 Course Applied Mathematics Topic A - Honours Coordinating Unit School of Mathematical Sciences Term Semester 1 Level Undergraduate Location/s North Terrace Campus Units 3 Contact Up to 2.5 hours per week Available for Study Abroad and Exchange Y Restrictions May only be presented towards some Engineering Programs Course Description Please contact the School of Mathematical Sciences for further details, or view course information on the School of Mathematical Sciences web site at http://www.maths.adelaide.edu.au
Course Coordinator: Dr Trent Mattner
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning OutcomesIn 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.
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)
all 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
Recommended ResourcesPope, S. B., Turbulent Flows. Cambridge University Press, 2009.
Online LearningThis 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: https://myuni.adelaide.edu.au/webapps/login/
Learning & Teaching Activities
Learning & Teaching ModesThis 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 SummaryLecture Outline
Schedule 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 RequirementsNone.
The University's policy on Assessment for Coursework Programs is based on the following four principles:
- Assessment must encourage and reinforce learning.
- Assessment must enable robust and fair judgements about student performance.
- Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
- Assessment must maintain academic standards.
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 RequirementsAn aggregate score of at least 50% is required to pass the course.
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%
SubmissionAssignments will have a maximum two week turn-around time for feedback to students.
Grades for your performance in this course will be awarded in accordance with the following scheme:
M11 (Honours Mark Scheme) Grade Grade reflects following criteria for allocation of grade Reported on Official Transcript Fail A mark between 1-49 F Third Class A mark between 50-59 3 Second Class Div B A mark between 60-69 2B Second Class Div A A mark between 70-79 2A First Class A mark between 80-100 1 Result Pending An interim result RP Continuing Continuing CN
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.
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 (http://www.adelaide.edu.au/policies/101/) 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.
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