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Partial differential equations and their classification; boundary and initial conditions; analytical solution methods. Introduction to computational solution techniques and packages in solid mechanics (FEM), fluid dynamics (CFD) and heat/mass transfer.
To extend students’ exposure to, and understanding of the significance and solution of differential equations by adding partial differential equations (PDEs) to the already-familiar ordinary differential equations. Based on this mathematical understanding of PDEs, students will then become familiar with the underlying principles of the numerical solution techniques of these same equations that are utilised in commonly-employed computational packages such as COMSOL, used not in a “black box” manner but, rather, with an appreciation of the underlying mathematics and numerical techniques that are embedded within them. This understanding of computational methods will be further augmented by the students’ own development and implementation of standard algorithms for numerical solution of PDEs.
On successful completion of this course students will be able to:Understand and apply the basic FEA elements (bar, beam and frame elements) and formulations that are readily extended from 2D to 3D analysis, including the major limitations of the methods.Be able to code, in Matlab or similar, the basic FEA assembly and analysis methods, and apply them to solve problems.Recognise and classify the different types of partial differential equations (elliptic, parabolic and hyperbolic)Recognise and apply, as appropriate, Dirichlet and Neumann boundary conditions (and, for unsteady state, initial conditions)Use separation of variables solution method where applicableUnderstand and apply D’Alembert solution and characteristicsUnderstand and appreciate the essential components of the PDE models for classical mechanical systems: steady and transient heat transfer; potential and transient flow; elastic bending and waves.Confidently apply standard analytic solution methods to the classical PDEs used in mechanical analysis.Appreciate properties and limitations of any numerical solution method: accuracy, consistency, convergenceRecognise and apply different numerical solution terminology and techniques: Spatial discretization; finite differences; weighted residual methods; polynomial interpolating/weighting functions; finite element methods; finite volumesUnderstand the strategies used in coding computational methods to maximize efficiency and minimize processing time. Productively and confidently use generic computational packages (e.g. COMSOL) in the solution of “real world” problems in solid mechanics, fluid flow, and heat or mass transferAppreciate both the benefits and the limitations of such packages by comparison of numerical solutions with analytical solutions in situations where this is possible.
This course will provide students with an opportunity to develop the Graduate Attributes specified below:
Critically competent in a core academic discipline of their award
Students know and can critically evaluate and, where applicable, apply this knowledge to topics/issues within their majoring subject.
EMTH210, EMTH271 orEMTH211, ENME202
Students must attend one activity from each section.
and James Hewett
Advanced modern engineering mathematics;
Prentice Hall, 2011.
Patankar, Suhas V;
Numerical heat transfer and fluid flow;
Hemisphere Pub. Corp ; McGraw-Hill, 1980.
Zienkiewicz & Taylor;
The finite element method for solid and structural mechanics;
Harassment* Harassment of any sort will not be tolerated. Each UC student is here to learn and to experience a friendly and supportive community.* It is every student's right to expect: respect and courtesy from staff and other students, including freedom from harassment of any sort; fair treatment; the ability to speak out about any issues that concern them, without fear of consequences for their safety and well-being.* Furthermore, each student has the responsibility to: respect the rights and property of others; attend to their own health and safety, and that of others; and behave in a manner towards each other that does not reflect badly on the student body or the University.* If you, or someone you know, has experienced harassment, please talk to your lecturers, directors of study, or head of department.Dishonest Practice* Plagiarism, collusion, copying, and ghost writing are unacceptable and dishonest practices.* Plagiarism is the presentation of any material (test, data, figures or drawings, on any medium including computer files) from any other source without clear and adequate acknowledgment of the source.* Collusion is the presentation of work performed in conjunction with another person or persons, but submitted as if it has been completed only by the named author(s).* Copying is the use of material (in any medium, including computer files) produced by another person(s) with or without their knowledge and approval.* Ghost writing is the use of another person(s) (with or without payment) to prepare all or part of an item submitted for assessment.Do not engage in dishonest practices. The Department reserves the right to refer dishonest practices to the University Proctor and where appropriate to not mark the work.The University regulations on academic integrity and dishonest practice can be found here.
Domestic fee $975.00
International fee $5,500.00
* Fees include New Zealand GST and do not include any programme level discount or additional course related expenses.
For further information see