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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: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 applicableApply Laplace transforms in the solution of the diffusion equationUnderstand 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.
EMTH210, EMTH271 or EMTH211, ENME202, ENME204
ENME342; EMTH391
Mathieu Sellier
Geoff Rodgers
James, Glyn; Advanced modern engineering mathematics ; 4th ed; Prentice Hall, 2011.
Patankar, Suhas V; Numerical heat transfer and fluid flow ; Hemisphere Pub. Corp ; McGraw-Hill, 1980.
Zienkiewicz & Taylor; The Element Model for Solid and Structural Mechanics ; Butterworth-Heinemann, 2005.
Domestic fee $808.00
International fee $4,550.00
* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.
For further information see Mechanical Engineering .