## CIVE3650 Computational Methods for Civil Engineering

### 10 creditsClass Size: 70

Module manager: Dr. Amirul Khan
Email: a.khan@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2021/22

### Pre-requisites

 CIVE1560 Engineering Mathematics and Modelling 1 CIVE2560 Engineering Mathematics and Modelling 2

This module is not approved as a discovery module

### Objectives

To provide students with the background theory and hands on experience of the computational methods for modelling engineering problems (that typically involve numerically solving differential equations). The module requires students to develop experience of commercial tools/software to solve real engineering problems. Methods introduced will include, to varying extents, the Finite Difference (FDM) and Finite Volume (FVM) Methods & Finite Element methods (FEM).

The module objective is that students will:

(i) develop an understanding of the principles of discretisation of continuum engineering problems represented by governing differential equations using different numerical techniques.

(ii) develop appreciation of physical situations where the above mathematical techniques are useful;

(iii) be able to choose, formulate and implement appropriate numerical methods for solving Engineering problems that are formulated as partial differential equations (PDEs) and be able to interpret, analyse and evaluate results from numerical computations;

(iv) develop awareness of challenges, limitations and common issues that are important when undertaking computational modelling of engineering problems

(v) develop confidence in using a commercial solver/code/tools (e.g. FLUENT, ABAQUS, COMSOL, Dynamic thermal modelling tools, DualSPHysics, MATLAB etc.) to solve problems arising in Civil Engineering formulated as differential equations (such as heat transfer and transport, linear elasticity problems;), This will be undertaken in the form of a student mini project.

Learning outcomes
On completion of this module students will be able to:

1. develop knowledge and understanding of basic mathematical principles to underpin numerical techniques used in modern engineering practice (including, Finite Difference, Finite Volume & Finite Element methods);

2. appreciate when it is necessary to use numerical methods and develop knowledge and understanding of the difference between linear and nonlinear equations particularly the difference between parabolic, elliptical and hyperbolic PDEs.

3. formulate simple finite difference expressions using Taylor series and apply the principles of finite difference and finite volume methods to a range of common engineering problems involving ordinary and partial differential equations and to predict distributions of key variables.

4. develop and gain experience using computational tools/software (e.g. MATLAB) to solve typical field problems (e.g. fluid flow, heat transfer)

5. develop comprehension of finite difference and finite element techniques being used in solving engineering problems and able to list main steps of developing a model using the finite difference and finite volume method

6. be able to analyse linear and nonlinear systems of partial differential equations, using finite difference and finite element methods. Solve time dependent problems using the methodologies of finite difference and finite element methods formulated as explicit and implicit time discretisation methods, particularly linking it to commercial codes.

7. Undertake investigative numerical methods project using a commercial code

### Syllabus

Brief Review Numerical methods for ODE’s
Numerically defined functions: solution techniques, difference formulae, interpolation functions; Taylor's series and truncation error; Numerical differentiation: boundary value problems, initial value problems, Euler's method and higher order Runge-Kutte methods.

Principles of Meshing and its implications on discretisation accuracy.

Initial- and boundary-value problems for ordinary differential equations using shooting techniques and difference methods.

Numerical solution of partial differential equations using difference methods, but also introduction to the finite element method if time allows.

Explicit and implicit schemes are introduced; these are focused on one-dimensional transient problems (but higher dimension examples are discussed for context). Use of Fourier stability analysis.

Stationary problems in two dimensions. The examples and problems are taken mainly from the following fields: Heat transfer, dynamics, elasticity and fluid mechanics.

MATLAB is used in the course; in the examples, for solving exercises and where appropriate in the mini project.

An appropriate computational tool/software will be used as part of the mini-project such that students are required to solve problems that use the theoretical concepts and principles introduced within the module, to analyse and solve an engineering problem.

### Teaching methods

 Delivery type Number Length hours Student hours On-line Learning 6 2.00 12.00 Problem Based Learning 1 25.00 5.00 Class tests, exams and assessment 2 6.00 12.00 Group learning 4 1.00 4.00 Lecture 11 1.00 11.00 Tutorial 3 2.00 6.00 Independent online learning hours 20.00 Private study hours 30.00 Total Contact hours 50.00 Total hours (100hr per 10 credits) 100.00

### Private study

Review of lecture materials
Directed online study preparatory work for mini project.
Completing mini project (include writing Matlab code)
Undertaking preparation for workshops and completing the associated formative tasks

### Opportunities for Formative Feedback

In class interactivity
Meetings during mini-project

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment Project Mini project that makes use of a commercial computer program/code to numerically analyse/ solve an engineering problem 50.00 Problem Sheet 1 problem sheet 0.00 Total percentage (Assessment Coursework) 50.00

Re-sit - 100% online time-limited assessment

Exams
 Exam type Exam duration % of formal assessment Online Time-Limited assessment 2 hr 00 mins 50.00 Total percentage (Assessment Exams) 50.00

Re-sit - 100% online time-limited assessment