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Module Code: ENG3160 Module Title: NUMERICAL METHODS FOR CIVIL ENGINEERING APPLICATIONS
 Module Provider: Civil, Chemical & Enviromental Eng Short Name: ENG3160 Level: HE3 Module Co-ordinator: CLARK PA Prof (C, C & E Eng) Number of credits: 15 Number of ECTS credits: 7.5
Module Availability
Semester 1 and 2
Assessment Pattern
 Unit(s) of Assessment Weighting Towards Module Mark( %) 2 hour Examination (Assessment of the following learning outcomes: 1,2,3 and 5.) 55% Coursework   Development and testing of a Matlab program to solve Poisson's equation by two different numerical methods. (Assessment of the following learning outcomes: 4, and, in part 2 and 3.) 15% Development and testing of a Matlab program to solve the shallow water equations, evaluating stability and accuracy of the method chosen. (Assessment of the following learning outcomes: 5 and 6, in part, 2,3 and 4) 30% Qualifying Condition(s)  Completion of the progress requirements of Level HE2 An overall mark of 40% is required to pass the module
Module Overview

The majority of problems facing Engineers require mathematical models which either do not have analytic solutions for the range of conditions met in practice or, even where they do, are so complex that hand-solution is impractical. Many of these problems can be expressed as partial differential equations. Use of computers to solve problems using approximate numerical methods is thus an every-day part of engineering. This module covers the principles behind a range of methods for both formulating and solving partial differential equations as well as expanding on previous knowledge of solution of algebraic and ordinary differential equations. It also provides a grounding in the implementation and testing of practical solution methods.

Prerequisites/Co-requisites
Completion of the progress requirements of Level HE2
Module Aims

To provide a sound understanding of the basic tools available for the numerical solution of a range of partial differential equations encountered by engineers.  To familiarize the students with techniques used to design, implement and test numerical solutions.

Learning Outcomes

On successful completion of the module you should be able to:

1. Describe the basic mathematical ideas behind finite difference, finite volume or finite element techniques.

1. Chose an appropriate technique (finite difference, finite volume or finite element) to solve a common partial differential equation.

1. Design an algorithm to solve a common partial differential equation, taking into account appropriate boundary conditions.

1. Implement this algorithm in Matlab, including implementing any solution algorithm.

1. Analyse the accuracy and, where appropriate, the stability of a numerical solution technique.

1. Use test problems to evaluate the accuracy, cost and where appropriate, the  stability of a numerical solution technique.
Module Content

Polynomial fitting and Taylor's expansion; interpolation and numerical integration (revision).

Solutions off systems of linear equations: Gaussian elimination with partial pivoting, LU factorization and inversion, iterative techniques (Gauss-Seidel, Jacobi, Successive over relaxation).

Finite difference approximations and difference operators. Order and accuracy of approximations.

Application of finite difference approximations to elliptic problems in one and two-dimensions.

Introduction to Finite Element Methods for elliptic problems.

Application of finite difference approximations to parabolic problems in one and two-dimensions. Time-stepping methods. Analysis of stability.

Introduction to hyperbolic problems; finite-difference approaches to linear and non-linear advection and conservation problems; stability analysis, numerical phase and group velocity. Shallow water equations; grid staggering. Introduction to finite volume methods.

Developing codes; validation, testing strategies, numerical convergence and accuracy.

Methods of Teaching/Learning

33 hours of lectures (11 semester 1, 22 semester 2), 22 hours of tutorial classes (11 semester 1, 11 semester 2), and 93 hours independent learning. 2 hour examination. Tutorials and coursework will include Matlab computer-based exercises.

Total student learning time 150 hours.

Selected Texts/Journals

Numerical Methods for Engineers, Steven C. Chapra and Raymond P Canale, 2005, McGraw-Hill

Numerical Methods for Mathematics, Science and Engineering, John H. Mathews, 1998, Prentice-Hall

Schaum's Outline of Finite Element Analysis, George R. Buchanan, 1995

Numerical Methods for Engineers and Scientists, Joe D. Hoffman, McGraw-Hill, 2001
Last Updated
29th September 2010

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